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Dr. Rajesh Kumar Pandey

Professor
Department of Mathematical Sciences,IIT BHU
Phone No(s): 9453897736
Email: rkpandey.mat@iitbhu.ac.in
Area of Interest: Numerical Methods for Integro-differential Equations; Wavelets; Fractional Derivatives; Image Processing
                    Vist my Website

    Prof. Rajesh Kumar Pandey received his M. Sc. degree in Mathematics from Banaras Hindu University and Ph. D. from Institute of Technology, Banaras Hindu University Varanasi in 2009. He is a Professor of Mathematical Sciences at the Indian Institute of Technology (Banaras Hindu University) Varanasi, Uttar Pradesh India. He is recipient of Indo-US fellowship and INSA Visiting Fellowship for the year 2012. He has also worked as Assistant Professor in Mathematics at BITS Pilani and Indian Institute of Information Technology Design and Manufacturing Jabalpur during July 2009—May 2014. He has published more than 80 research papers in refereed journals and guided 12 PhD students. His current areas of research include Medical Image Processing, Fractional Differential Equations, Numerical Analysis for Fractional Partial Differential Equations.

    Current Position:

    • Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi.

    Education:

    • ​Ph. D. Applied Mathematics:  Department of Applied Mathematics, Indian Institute of Technology (BHU) Varanasi.
    • M. Sc. Mathematics: Department of Mathematics, Banaras Hindu University, Varanasi.

    Postdoctoral Research Experience: 

    • Visiting Faculty as IUSSTF Research Fellow: Southern Illinois University Carbondale, Illinois, USA:  Sept. 30/2012 - July 17/ 2013 (Under INDO-US Science and Technology Forum).
    • Visiting Research Fellow: Department of Mathematical Informatics, The University of Tokyo, Tokyo, Japan (Nov/2010 - Dec/2010). 
    • IASc-INSA-NASI Summer Research Fellow: Physics & Applied Mathematics Unit, Indian Statistical Institute, Kolkata, India (May/2010 - July/2010).

    Experience: Teaching

    • Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi:  July 30, 2024-till date.
    • Associate Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi:  July 19, 2017-July 30, 2024.
    • Assistant Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi:  June 10, 2014-July 18, 2017.
    • Assistant Professor in Mathematics, Indian Institute of Information Technology Design & Manufacturing Jabalpur, Jabalpur:  July 09, 2009-June 09, 2014.
    • Lecturer in Department of Mathematics at Birla Institute of Technology and Science, Pilani (BITS-Pilani)-Goa Campus, Goa: Feb 2009 to June 2009.

    Courses Taught @IIT (BHU) Varanasi

    • Digital Image Processing
    • Numerical Techniques
    • Engineering Mathematics I
    • Mathematical Methods
    • Engineering Mathematics II
    • Calculus of Variations and Integral Equations

    Courses Taught at IIITDM Jabalpur

    • Wavelet Transforms & Applications 
    • Advanced Mathematical Methods 
    • Mathematics for Discrete Domain
    • Mathematics for Continuous & Discrete Domains

    Courses Taught at BITS - Pilani, Goa Campus

    • MATHS II (Linear Algebra & Complex Analysis)
    • Numerical Analysis

     

    • Numerical Methods for Fractional Integro-Differential Equations
    • Fractional Differential Equations
    • Image Processing. 

     

    Selected Journal Publications: 

    Fractional Differential Equations: 

    • S Kumari, R. K. Pandey, An efficient temporal approximation for weakly singular time-fractional semilinear diffusion-wave equation with variable coefficients, Numerical Algorithms, 1-49 (2024)
    • S. Kumar, K. Kumar, R. K. Pandey, Y. Xu, Legendre collocation method for new generalized fractional advection-diffusion equation, International Journal of Computer Mathematics, (2024) 1-23.
    • S. Kumari, R. K. Pandey, Alternating direction implicit approach for the two-dimensional time fractional nonlinear Klein-Gordon and Sine-Gordon problems, Communications in Nonlinear Science and Numerical Simulation, 130 (2024) 107769.
    • S. Kumari, R. K. Pandey, Single-term and multi-term nonuniform time-stepping approximation methods for two-dimensional time-fractional diffusion-wave equation, Computers and Mathematics with Applications, 151 (2023) 359-383.
    • D. Singh, R. K. Pandey, S. Kumari, A fourth order accurate numerical method for non-linear time fractional reaction–diffusion equation on a bounded domain, Physica D: Nonlinear Phenomena 449 (2023), 133742.
    • E. Goel, R. K. Pandey, S. Yadav, O. P. Agrawal, A numerical approximation for generalized fractional Sturm–Liouville problem with application, Mathematics and Computers in Simulation, 207 (2023) 417-436.
    • D. Singh, F. Sultana, R. K. Pandey, Approximation of Caputo-Prabhakar derivative with application in solving time fractional Advection-Diffusion equation, International Journal for Numerical Methods in Fluids, 94(7) (2022) 896-919.
    • D. Pandey, R. K. Pandey, R. P. Agarwal, Numerical Approximation of Fractional Variational Problems with Several Dependent Variables Using Jacobi Poly-Fractonomials, Mathematics and Computers in Simulation, 203(2023) 28-43. 
    • K Kumar, R. K. Pandey, F Sultana, Numerical schemes with convergence for generalized fractional integro-differential equations, Journal of Computational and Applied Mathematics 388 (1), (2021) 113318.
    • S. Yadav, R. K. Pandey, P. K. Pandey, Numerical Approximation of Tempered Fractional Sturm-Liouville Problem with Application in Fractional Diffusion Equation, International Journal for Numerical Methods in Fluids, 93 (3) (2021) 610-627.
    • F. Sultana, D. Singh, R. K. Pandey, D. Zeiden, Numerical Schemes for a Class of Tempered Fractional Integro-differential Equations, Applied Numerical Mathematics, 157 (2020) 110-134.
    • P. K. Pandey, R. K. Pandey, O. P. Agrawal, Variational Approximation for Fractional Sturm-Liouville Problem, Fractional Calculus and Applied Analysis, 23(3) (2020) 861-874.
    • S Yadav, R K Pandey, Numerical Approximation of Fractional Burgers Equation with Atangana-Baleanu Derivative in Caputo Sense, Chaos Solitons & Fractals, 133 (2020) 109630-8.
    • A. Gupta, R. K. Pandey, Adaptive Huber scheme for weakly singular fractional integro-differential equations, Differential Equations and Dynamical Systems, 28 (2020) 527–538.
    • K. Kumar, R. K. Pandey and S. Yadav, Finite Difference Scheme for a Fractional Telegraph Equation with Generalized Fractional Derivative Terms, Physica A: Statistical Mechanics and its Applications, 535 (2019) 122271-15.
    • S. Yadav, R. K. Pandey, A. K. Shukla, and K. Kumar, High-Order Approximation for Generalized Fractional Derivative and Its Application, International Journal of Numerical Methods for Heat and Fluid Flow, 29(9) (2019), 3515-3534.
    • K Kumar, R K Pandey, S Sharma, Y.  Xu, Numerical scheme with convergence for a generalized time‐fractional Telegraph‐type equation, Numerical Methods for Partial Differential Equations 35 (3) (2019) 1164-1183.
    • H Singh, Rajesh K. Pandey, H M Srivastava, Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials, Mathematics, 7 (3) (2019) 224.
    • S. Yadav, R. K. Pandey, A. K. Shukla, Numerical approximations of Atangana–Baleanu Caputo derivative and its application , Chaos Solitons & Fractals, 118 (2019) 58-64.
    • A. K. Shukla, R. K. Pandey and Swati Yadav, Salt and Peper Noise Algorithm Based on Generalized Fractional Operator, International Journal of Pure and Applied Mathematics, 119 (16) (2018) 5147-5158.
    • S. Sharma, R. K. Pandey, Kamlesh Kumar, Collocation method with convergence for generalized fractional integro-differential equations, Journal of Computational and Applied Mathematics, 342 (2018) 419-430.
    • S. Sharma, R. K. Pandey, K. Kumar, Galerkin and Collocation Methods for Weakly Singular Fractional Integro-differential Equations, Iranian Journal of Science and Technology, Transactions A: Science, Accepted 2018 
    • K. Kumar, R. K. Pandey, S. Sharma, Numerical Schemes for the Generalized Abel’s Integral Equations, International Journal of Applied and Computational Mathematics,  4 (2) (2018) 68
    • K. Kumar, R. K. Pandey, S. Sharma, Approximations of Fractional Integrals and Caputo Derivatives with Application in Solving Abel’s Integral Equations, Journal of King Saud University-Science,  Accepted 2018
    • Kamlesh Kumar, R. K. Pandey, Shiva Sharma, Comparative study of three numerical schemes for fractional integro-differential equations, Journal of Computational and Applied Mathematics, 315 (2017), 287-302.
    • H Singh, R. K. Pandey, D Baleanu, Stable Numerical Approach for Fractional Delay Differential Equations, Few-Body Systems, 58 (6) (2017): 156
    • R. K. Pandey, Shiva Sharma and Kamlesh Kumar, Collocation method for generalized Abel’s integral equations, Journal of Computational and Applied Mathematics, 302 (2016), 118-128.
    • R. K. Pandey and O. P. Agrawal, Numerical Scheme for a Quadratic Type Generalized Isoperimetric Constraint Variational Problems With A-Operator, ASME Journal of Computational and Nonlinear Dynamics, , Vol. 10, (2015), pp. 021003-6
    • R. K. Pandey, S. Suman, K. K. Singh, O. P. Singh, An approximate method for Abel inversion using Chebyshev polynomials, Applied Mathematics & Computation, 237(2014), 120-132.
    • R. K. Pandey, N. Kumar, A. Bhardwaj and G. Dutta, Solution of Lane-Emden type equations using Legendre operational matrix of differentiation, Applied Mathematics and Computation,218 (14) (2012) 7629-7637.
    • R. K. Pandey, N. Kumar, Solution of Lane-Emden type equations using Bernstein Operational matrix of Differentiation, New Astronomy 17 (2012) 303-308. 
    • R. K. Pandey and B. N. Mandal, Numerical solution of a system of generalized Abel integral equations using Bernstein polynomials, Journal of Advanced Research in Scientific Computing 2 (2) (2010) 44-53.
    • D. Singh, R. K. Mishra, V. K. Singh, R. K. Pandey, Bad Data pre-filter for State Estimation, Electrical Power and Energy Systems, 32 (2010) 1165-1174.
    • O. P. Singh, V. K. Singh, R. K. Pandey, An efficient and stable algorithm for numerical evaluation of Hankel transforms, Journal of Applied Mathematics & Informatics 28 (5-6) (2010) 1055-1071.
    • R. K. Pandey, O. P. Singh, V. K. Singh, D. Singh, Numerical evaluation of    Hankel transforms using Haar wavelets, International Journal of Computer Mathematics 87 (11) (2010) 2568-2573. 
    • R. K. Pandey, V. K. Singh, O. P. Singh, A New Stable Algorithm for Hankel transform using Chebyshev Wavelets, Communications in Computational Physics 8(2) (2010) 351-373.
    • R. K. Pandey, O. P. Singh, V. K. Singh., A Stable Algorithm for Numerical evaluation of Hankel transforms using Haar wavelet, Numerical Algorithms 53(4) (2010) 451-466. 
    • V. K. Singh, R. K. Pandey, S. Singh, A Stable Algorithm for Hankel transform using hybrid of Block pulse and Legendre polynomials, Computer Physics Communications 181 (2010) 1-10. 
    • O. P. Singh,V. K. Singh, R. K. Pandey, New stable numerical inversion of  Abel’s integral equation using almost Bernstein operational matrix, Journal of Quantitative Spectroscopy and Radiative Transfer 111 (2010) 245-252.
    • R. K. Pandey, O. P. Singh, V. K. Singh, Numerical solution of system of Volterra  integral equations using Bernstein polynomials, International Journal of  Nonlinear Sciences and Numerical Simulation 10 (7) (2009) 691-695.  
    • O. P. Singh, V. K. Singh, R. K. Pandey, A New Stable Algorithm for Abel   inversion Using Bernstein Polynomials, International Journal of Nonlinear  Sciences and Numerical Simulation 10 (5) (2009) 681-685. 
    • O. P. Singh, R. K. Pandey, V. K. Singh, An analytic algorithm for Lane –Emden  equations arising in Astrophysics using MHAM, Computer Physics Communications 180 (2009) 1116-1124.
    • R. K. Pandey, V. K. Singh, O. P. Singh, An improved method for computing Hankel transform, Journal of The Franklin Institute 346 (2)(2009) 102-111.  
    • R. K. Pandey, O. P. Singh, V.K. Singh, Efficient algorithms to solve singular integral equations of Abel type, Computer & Mathematics with Applications 57(4) (2009) 664- 676.
    • V. K. Singh, O. P. Singh, R. K. Pandey, Efficient algorithms to compute Hankel transform using wavelets, Computer Physics Communications 179 (2008) 812-818.                                                                       
    • V. K. Singh, O. P. Singh, R. K. Pandey, Numerical evaluation of Hankel transforms by using linear Legendre multi-wavelets, Computer Physics Communications 179 (2008) 424-429.                                                                                   

    Image Processing:

    • U. Mishra, A. Agrawal, J. C. R. Mathew, R. K. Pandey, P. Chattopadhyay, An efficient approach for image de-fencing based on conditional generative adversarial network, Signal, Image and Video Processing, 2022, doi: 10.1007/s11760-022-02215-1.
    • A K Shukla, R K Pandey, R B Pachori, A fractional filter based efficient algorithm for retinal blood vessel segmentation, Biomedical Signal Processing and Control, 59, (2020) 101883-15.
    • A K Shukla, R K Pandey, S Yadav, Adaptive Fractional Masks and Super Resolution Based Approach for Image Enhancement, Multimedia Tools and Applications, 2020 (doi.org/10.1007/s11042-020-08968-6).
    • A. K. Shukla, R. K. Pandey, P K Reddy, Generalized fractional derivative based adaptive algorithm for image denoising, Multimedia Tools and Applications, 79 (2020), 14201–14224.
    • A. K. Shukla, R. K. Pandey, R. B. Pachori, Generalized fractional filter based algorithm for image denoising, Circuits, Systems, and Signal Processing, 39(1) (2020) 363-390
    • A. K. Shukla, R. K. Pandey and Swati Yadav, Salt and Peper Noise Algorithm Based on Generalized Fractional Operator, International Journal of Pure and Applied Mathematics, 119 (16) (2018) 5147-5158.
    • K. K. Singh, M. K. Bajpayee and R. K. Pandey, A novel approach for enhancement of geometric and contrast resolution properties of low contrast images, IEEE/CAA Journal of Automatica Sinica, 5(2) (2018) 628-638.
    • K. K. Singh, M. K. Bajpayee, R K Pandey and P. Munshi, A novel non-invasive method for extraction of geometrical and texture features of wood, Research in Nondestructive Evaluation, 28 (3) (2017), 150-167  DOI: 10.1080/09349847.2016.1148214.
    • A. Kumar, K. Ranjeet and R. K. Pandey, Beta Wavelet Based ECG Signal Compression using Lossless Encoding with Modified Thresholding, Computer & Electrical Engineering, 39(1) (2013) 130 - 140.
    • K. Ranjeet, A. Kumar, and R. K. Pandey, Electrocardiogram Signal Compression using Beta Wavelets, Journal of Mathematical Modeling and Algorithms 11(3) (2012) 235-248.
    • K. Ranjeet, A. Kumar, R. K. Pandey, ECG signal compression using different techniques, Communications in Computer and Information Science, 125 (2) (2011) 231-241.

    Conference Publications:

    • S. Sharma and R. K. Pandey, Jacobi collocation method for fractional-integro differential equations, Vol. 2, pp. 854-862, Proceedings of the International Conference on Fractional Differentiation and its Applications, Novi Sad, Serbia, July 18 - 20, 2016.
    • R. K. Pandey and O. P. Agrawal, Comparison of Four Numerical Schemes for Isoperimetric Constraint Fractional Variational Problems with A-Operator, ASME 2015 International Design & Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2015), Boston, MA, USA, August 2-5, 2015, Paper No. DETC2015-46570.
    • K. K.Singh, M. K.Bajpai, and R. K. Pandey, A Novel Approach For Edge Dectection of Low Contrast Satellite Images, Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., XL-3/W2, 211-217, doi:10.5194/isprsarchives-XL-3-W2-211-2015, 2015.
    • Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey, Edge Detection in Low Contrast Images, XIII International Conferences on Image Processing 2015, Zurich, Switzerland, January, 13-14, 2015.
    • K K. Singh, R. K. Pandey and Suraj Suman, Fractional order differentiator using Legendre polynomials, IEEE Proceeding of 5th International Conference Confluence: The Next Generation Information Technology Summit (Confluence), 2014, pp. 246-250. 
    • R. K. Pandey and O. P. Agrawal, Numerical scheme for generalized isoperimetric constraint variational problems with A-operator, Proceeding of the 2013 ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications, Portland, Oregon, USA, August 4–7, 2013, Paper No. DETC2013-12388, pp. V004T08A017; 6 pages (received Best Paper Award).
    • Koushlendra K. Singh, R. K. Pandey and B. N. Mandal, An analytical method for solving singular integral equations of Abel type, International Conference on Modeling, Optimization and Computing-2012, Procedia EngineeringVolume 38, 2012, Pages 2726-2738.
    • K. Ranjeet, A. Kuamr, R. K. Pandey, ECG Signal Compression using Optimum Wavelet Filter Bank Based on Kaiser Window, Procedia Engineering, Volume 38, 2012, Pages 2889-2902.
    • A. Setia, R. K. Pandey, Laguerre Polynomials Based Numerical Method to Solve a System of Generalized Abel Integral Equations,   Procedia Engineering, Volume 38, 2012, Pages 1675-1682
    • R. K. Pandey, V. K. Singh, S. Singh: Computation of Fourier Bessel Transform Using Hybrid Functions. 1186-1199, Proceedings of the 5th Indian International Conference on Artificial Intelligence, IICAI 2011, Tumkur, Karnataka State, India, December 14-16, 2011. IICAI 2011, ISBN 978-0-9727412-8-6.
     
    Edited Books:
     
    • H Singh, HM Srivastava, R K Pandey, Special Functions in Fractional Calculus and Engineering, CRC Press 2023.
    • T. N. Dinh, Shyam Kamal and Rajesh Kumar Pandey, Fractional-Order System: Control Theory and Applications, March 2023, ISBN 978-3-0365-6422-7 (hardback); ISBN 978-3-0365-6423-4 (PDF): https://doi.org/10.3390/books978-3-0365-6423-4
    • H. Sharma, V. K. Vyas, R. K. Pandey, M. Prasad, Proceedings of the International Conference on Intelligent Vision and Computing (ICIVC 2021), Springer Cham, https://doi.org/10.1007/978-3-030-97196-0
     
    Book Chapters:
    • Chapter 12: “Stable Algorithm for Computation of Hankel Transform using Chebyshev Wavelets” Wavelets: Classification, Theory and Applications. ISBN: 978-1-62100-308-3 (Imprint: NOVA) 2011.
    • Chapter 8: “Numerical Solution of a System of Generalized Abel Integral Equations” Applied Singular Integral Equations. ISBN: 978-1-57808-710-5 (CRC Press) 2011.

     

    • The Research project entitled “Approximation Methods for Generalized Sturm-Liouville Problems” has been sanctioned by SERB, Govt. of India of Rs. 6,60,000.00 for a period of three years (2023-2026).
    • The research project entitled "Approximation Methods For Problems In Fractional Calculus Of Variations" has been sanctioned by SERB , Govt. of India of Rs. 2156264.00 for a period of three years (2019-2022).
    • Coordinator for Mathematics, AICTE Project on Model curriculum preparation for UG Engg. courses for AICTE affiliated Engg. Colleges. Amount:  Rs. 1100000 approx. (2017)
    • The research project entitled "Development of solution methods for Abel's integral equation and Generalized Abel's integral equation" has been sanctioned by National Board of Higher Mathematics, DAE, Govt. of India of Rs. 332500.00 for a period of three years (2016-2019).
    • Awarded SERC Young Scientist Project 2012 (Under DST Fast Track Scheme):  The project entitled “Wavelets and operational matrix based techniques for integral equations” has been approved by SERB under SERC Fast track scheme for Young Scientist in Mathematical Sciences. (Amount:   Rs. 10,20,000/-)
    • Research Initiation Grant sanctioned by Indian Institute of Technology (BHU) of Rs.9, 63,889.00
     

     

    Name of Student
    		 
    Thesis Title / Area of Research
    		 
     Status
    		 
    Dr. Koushlendra Kumar Singh
 (Assistant Professor in Computer Science & Engg., NIT Jamshedpur)
    		 
    Chebyshev Polynomial Based Approximation of an Efficient Fractional Order Mask for Different Image Processing Applications
    		 
    Awarded 2016
    		 
    Dr. Harendra Singh
 (Assistant Professor in Mathematics at Ghazipur PG College, Ghazipur UP )
    		 
    Weak Asymptotic Approach To Conservation Laws and Fractional Partial Differential Equation
    		 
    Awarded 2016
    		 
    Dr. Kamlesh Kumar
    		 
    Approximations of Fractional Derivatives with Applications in Solving Integral and Integro-Differential Equations
    		 
    Awarded August 2018
    		 
    Dr. Shiva Sharma
    		 
    Projection Approximation For Weakly Singular Integral and Integro-Differential Equations
    		 
    Awarded December 2018
    		 
    Dr. Anil Kumar Shukla
    		 
    Newly Introduced Fractional Filters For Image processing Applications
    		 
    Awarded August 2020
    		 
    Dr. Swati Yadav

    (Post Doctoral Fellow at NTNU Gloshaugen, Trondheim, Norway)

    		 
    Numerical Schemes for Some Fractional Partial Differential Equations
    		 
    Awarded March 2021
    		 
    Dr. Prashant Kumar Pandey
    		 
    Approximation Methods for Fractional Sturm-Liouville Problems
    		 
    Awarded April 2022
    		 
    Dr. Sandeep Kumar

    Collocation Approximation For Fractional Integro-Differential And Sub-Diffusion Equations

    		 
    Awarded June 2023
    		 
    Dr. Deeksha Singh
    		 
    High-Order Discretization Methods For Fractional Diffusion Models

    Awarded Oct. 2023
    Dr. Divyansh Pandey Approximation Methods for Fractional Variational and Sturm-Liouville Problems Awarded April 2024 
    Dr. Sarita Kumari
    		Analysis of Discretization Methods for Time-Fractional Diffusion and Diffusion-Wave Equations with Weak Initial Singularity 
    Awarded June 2024
    		 
    Eti Goel
    		 
    Numerical Approximations for Some Fractional Sturm-Liouville Problems
    		 
    Thesis Submitted (Sept. 2024)
         

     

    • Convener, Training and Placement, Mathematical Sciences, IIT(BHU) Varanasi for 2021-22, 2022-23 & 2023-24.
    • Convener, Space Committee, Mathematical Sciences, IIT(BHU) Varanasi for 2022-23.
    • Member, R&D Committee, IIT(BHU) Varanasi for 2022-23.
    • Member, DUGC, Mathematical Sciences, IIT(BHU) Varanasi for 2018-19, 2021-22 & 2022-23.
    • Member, Faculty Forum IIT (BHU) Varanasi 2017-18 & 2022-23.
    • Member, DPGC, Mathematical Sciences, IIT (BHU) Varanasi for year 2020-21.
    • Convener, DPGC, Mathematical Sciences, IIT (BHU) Varanasi for year 2019-20.
    • Member, Staff Committee, Mathematical Sciences, IIT(BHU) Varanasi for 2018-19.
    • Chairman, Ph D Admission, Mathematical Sciences,IIT (BHU) Varanasi for Odd Semester 2018-19.
    • Admin. Warden, Dr. S. Ramanujan Hostel, Indian Institute of Technology (BHU) Varanasi from May 30, 2018-May 31, 2021.
    • Member, DPGC, Mathematical Sciences, IIT (BHU) Varanasi for year 2017-18 & 2018-19.
    • Member, Time Table Committee, Mathematical Sciences, IIT (BHU) Varanasi.
    • Convener, Web Committee, Mathematical Sciences, IIT (BHU) Varanasi.
    • Warden, Aryabhatt Hostel, Indian Institute of Technology (BHU) Varanasi from August 10, 2015-May 29, 2018.
    • Coordinator-Examination Cell, IIITDM Jabalpur from Dec.2013 – May 2014.
    • Coordinator-Time Table, IIITDM Jabalpur from Dec.2013 – May 2014.
    • Warden In-charge, Hall of Residence-III, IIITDM Jabalpur from July 9, 2010 – July 19, 2012.
    • Member, Student Prizes & Awards Committee of Senate, IIITDM Jabalpur 2010.

    Upcoming Conference

    To be updated...

    Editorial Assignments

    • Lead Guest Editor for special issue "Computational Methods for Mathematical Models in Heat, Fluid Flow and Allied Topics with Applications”  in the journal International Journal of Numerical Methods for Heat and Fluid Flow
    • Lead Guest Editor for the special issue "RAAM 2024 Emerging Mathematical and Computational Methods for Non Linear Phenomena​​” in the journal International Journal of Applied Nonlinear Science
    • Guest Editor for the special issue "Emerging Trends in Computational and Machine Learning Approaches for Problems in Signal and Image Processing” in the journal SN Computer Science
    • Guest Editor for the special issue of RAAM 2024 in the journal Critical Reviews in Biomedical Engineering. 
    • Guest Editor for the Special Issue  "Fractional-Order System: Control Theory and Applications"  of the Journal  "Fractal and Fractional" (https://www.mdpi.com/journal/fractalfract/special_issues/foscta)

    Conference/Workshop Organized

    • 2nd International Conference on Recent Advances in Applied Mathematics (RAAM 2024) During July 03-05, 2024 at Department of Mathematical Sciences, IIT(BHU) Varanasi.  https://conferences.iitbhu.ac.in/RAAM2024/
    • Organized International Workshop on "Fractional Derivatives: Theory & Computations with Applications (FDTCA 2021)" at Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi, during November 12-14, 2021 in online mode: https://conferences.iitbhu.ac.in/FDTCA2021/  
    • Organized AICTE Short Term Course on Computational Methods for Integral and Differential Equations(CMIDE 18) during 10-16, 2018.
    • Organized GIAN Course on Fractional Derivatives and Its Applications during Jan. 30-Feb.03, 2018 at Department of Mathematical Sciences, IIT (BHU) Varanasi.
    • AICTE QIP Short term Course on Advanced Numerical and Analytical Methods for Engineers and Scientists (NAMES) 2017 during Jan. 12-18, 2017 at Department of Mathematical Sciences, IIT (BHU) Varanasi.
    • Workshop on wavelets and its Applications (WoW) during July 12-15, 2012 at IIITDM Jabalpur.

     Membership

    • Ramanujan Mathematical Society (Life Member)
    • Indian Mathematical Society (Life Member)
    • Academy for Progress of Mathematics, BHU, Varanasi
    • Treasurer, Mathematics & Computing Society, Mathematical Sciences, IIT(BHU) Varanasi 
    • International Association of Engineers (IAENG)

    Visit Abroad / Lectures Delivered

     

    • Delivered an Invited talk entitled “Retinal Blood Vessel Segmentation: A Mathematical Approach” on Dec. 10, 2024 in a Short Term Course on "Transforming Healthcare with AI-Driven Drugt Discovery” under the IDAPT Hub Foundation during Dec. 9-13, 2024 held at Dept. of Pharmacy, IIT(BHU) Varanasi. 
    • Delivered a Keynote lecture entitled “Fractional Filter Based Approach for Retinal Blood Vessel Segmentation” on Dec. 07, 2024 in 6th International Conference on Deep Learning, Artificial Intelligence and Robotics (ICDLAIR) -2024 (in Hybrid Mode) scheduled during 06-08 Dec' 2024, in the Department of Computer Science & Engineering, NIT Kurukshetra, Haryana, India. 
    • Delivered an Invited talk entitled “ Fractional Filter And Line Detector Based Approach for Retinal Blood Vessel Segmentation” on Nov. 30, 2024  in Annual Conference of Indian Society for Mathematical Modeling and Computer Simulation (ISMMACS) and International Conference on Differential Equations: Theory,Computation and Applications held at South Asian University New Delhi during November 29 – December 1, 2024.
    • Delivered and Invited talk on “Numerical scheme for a two-dimensional time fractional reaction–diffusion equation on a bounded domain” on Jan. 21, 2024 in Int. Symposium on Recent Trends in Numerical Methods for CDR Models, Fluids & Allied Topics, Jan. 20-21, 2024, organized by IIT Kanpur.
    • Delivered a Keynote talk entitled “Generalized Fractional Sturm-Liouville Problems: Numerical Approximations with Applications” on August 05, 2023 in the 6th International Conference on Mathematical Modelling, Applied Analysis, and Computation-2023 (ICMMAAC-23) organized by Department of Mathematics, Faculty of Science, JECRC Jaipur during August 3-5, 2023.
    • Delivered an Invited Talk on June 20, 2023 in the International Conference on Recent Advances in Applied Mathematics (RAAM 2023) BITS Pilani Dubai Campus, UAE during June 20-22, 2023.
    • Delivered an Invited Talk on July 01, 2022 in the International Conference on Dynamical Systems, Control and their Applications(ICDSCA-2022) held at Department of Mathematics at IIT Roorkee during July 1-3, 2022.
    • Delivered an Invited talk entitled “A Mathematical Approach for Medical Imaging (Retinal Blood Vessel Segmentation)” on May 24, 2022 in a High-End workshop (KARYASHALA) on “Artificial Intelligence In Drug Discovery: Quickening The Pace From Bench To Bedside” under the Accelerate Vigyan scheme of SERB during May 23-29, 2022 held at Dept of Pharmacy, IIT(BHU) Varanasi.
    • Delivered invited talk entitled “Approximations of Fractional Derivatives with Applications in Solving Fractional PDEs” on March 10, 2022 in the 25th Ramanujan Symposium-National Conference on Nonlinear Fractional Differential Equations during 9th -11th March, 2022.
    • Had served as General Chair and Keynote Speaker in International Conference on Intelligent Vision and Computing (ICIVC2021) organized by Sur University College Oman Technically Sponsored by Soft Computing Research Society during October 03-04, 2021.
    • Delivered an Invited Talk entitled “Fractional Calculus Applications in Image Processing” on Sept.25, 2021 in the refresher course on “Mathematical Tools for Physical and Computational Sciences” (Sept. 24-Oct08, 2021) organized by UGC-Human Resource Development Centre, Dr. Hari Singh Gaur Vishwavidyalaya Sagar Madhya Pradesh India.
    • Delivered an invited talk on “Approximation of Fractional Derivatives and Its Applications” on July 15, 2021 in one-week online Workshop on Differential Equations: Theory, Analysis and Applications with MATLAB(DETAAM-2021) at DIT University Dehradoon during July 12-16, 2021.
    • Delivered Conference Chair talk in Online National Conference on Exploring New Horizons of Mathematics in Context of Current Challenges held on Nov. 20, 2020 at Department of Applied Mathematics, Bhilai Institute of Technology, Durg.
    • Delivered an expert talk entitled “Fractional calculus for image processing applications” on Nov. 17, 2020 in QIP Sponsored Short-Term Course (STC) on “Wavelet via Matrices and its Applications in signals and image processing" from November 16-21, 2020 at IIT Indore.
    • Delivered an expert talk entitled “Fractional signal processing for medical applications” on Nov. 09, 2020 in TEQIP-III Sponsored Short-Term Course (STC) on “Artificial intelligence driven biomedical data analysis for disease diagnosis” at IIT Indore from 05-10 November, 2020.
    • Delivered an expert talk of two hours’ duration on Oct. 22, 2020 entitled “Fractional Filters for Medical Image Processing” in the TEQIP-III Sponsored Short-Term Course on Current Trends in Biomedical Signal and Image Processing organized by Discipline of Electrical Engineering, IIT Indore from 20-22 October, 2020. 
    • Delivered an Invited Talk entitled” Numerical Approximations for Isoperimetric Constraint Fractional variational Problems” on Aug.27, 2020 in TEQIP-III sponsored FDP entitled “Applications of Optimization Techniques in Science and Engineering” at BKBIET Pilani during 23-27 August, 2020 jointly organized by RTU Kota and BKBIET Pilani.
    • Had been an Invited speaker on “Fractional Calculus and Image Denoising” in the 3rd International Conference on Mathematical Modelling, Applied Analysis, and Computation-2020 (ICMMAAC-20) organized by Department of Mathematics, Faculty of Science, JECRC Jaipur during August 7-9, 2020. 
    • Delivered an Expert talk in TEQIP-III sponsored FDP on July 27, 2020 entitled “Newly Introduced Fractional Filters for Image Denoising”at VIT Jaipur Jointly organized by Rajasthan Technical University, Kota and Vivekananda Institute of Technology, Jaipur on “Applications of Mathematical Modelling in Science and Engineering” during 25th -27th July 2020.
    • Visited Department of Mathematics, Shanghai University, China during Dec. 10-12, 2019.
    • Delivered an Invited Lecture on “Numerical Approximation of Generalized Fractional Derivatives with Application” at The First International Conference Between University of Macau and Central
    • South University on Numerical Methods of PDEs during Dec 6 - 9, 2019 at School of Mathematics and Statistics, Central South University, Changsha, China.
    • Delivered Invited Lecture on “Fractional Filters and Its Application in Image Denoising” at International Conference on Computational Mathematics and its Applications (CMA 2019) during November 12-14, 2019 at Indian Institute of Technology Indore, India.
    • Delivered Invited Lecture on “Numerical Approximations for Isoperimetric Constraint Fractional Variational Problems” at International Conference on "Applied Mathematics and Computational Sciences (ICAMCS-2019) during October 17-19, 2019 at the Department of Mathematics, DIT University, Dehradun, India.
    • Delivered Expert Lecture on “Numerical Approximations of Fractional Derivatives with Applications " at KNIT, Sultanpur, Uttar Pradesh on July 18, 2019 under TEQIP –III Short Term Course.
    • Delivered Expert Lecture on “Numerical Approximations of Fractional Derivatives with Applications " at RCEW, Jaipur on June 26, 2019 under TEQIP-III sponsored by RTU Kota Rajasthan.
    • Chaired a Session and Delivered Invited talk on “Numerical Treatments to Isoperimetric Constraint Fractional Variational Problems” at International Conference on Applicable Analysis (ICAA) 2017 held at University of Delhi during Feb. 8-11, 2017.
    • Presented a paper in ICFDA 2016 at University of Novi sad, Novi sad, Serbia.
    • “ASME 2015 International Design & Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2015)”, held at Hynes Convention Centre, Boston, MA, USA, during August 2-5, 2015, Paper No. DETC2015-46570  Title: Comparison of Four Numerical Schemes for Isoperimetric Constraint Fractional Variational Problems with A-Operator
    • “The 5th International Conference on Scientific Computing and Partial Differential Equations (SCPDE14)”, held at Hong Kong Baptist University, Hong Kongduring December 8-12, 2014.Title: An Approximate Method for Fractional Differential Equations”
    • International Symposium on Fractional PDEs: Theory, Numeric and Applications Salve Regina University, USA during June 3 - 5, 2013. Title: Fractional Derivative and its Applications.
    • Fourth International Conference on Mathematical Sciences (ICM 2012) at United Arab Emirates University, UAE during March 11-14, 2012. Title: A New Method for Solving Fractional Differential Equations.
    • International Workshop on Wavelets, Frames and Applications: Dec. 15-21, 2011 Department of Mathematics, Kirori Mal College, University of Delhi, Delhi, India (Invited Talk).
    • 5th Indian International Conference on Artificial Intelligence (IICAI-11) Dec. 14-16, 2011, Siddaganga Institute of Technology, Tumkur, India
    • International Conference on Special Functions in the 21st Century: Theory and Applications (SF21), April 6-8, 2011(held at the Renaissance Washington Dupont Circle Hotel, 1143 New Hampshire Avenue NW) National Institute of Standards & Technology, Washington, DC, USA. (Invited Talk).

     

    • Reviewer for Mathematical Reviews/MathSciNet [ Reviewer Number: 122486]: 2016 onwards
    • Had been offered to join Corporate Planning, SAUDI ARAMCO (Saudi Arabian Oil Company) as Planning and Progress Analyst.
    • Best Research Paper Award for paper no. DETC 2013-12388 (Awarded by Mechatronic and Embedded Systems and Applications (MESA), committee of the ASME 2013 International Design Engineering Technical Conferences held at Portland, Oregon USA, August 4-7.)
    • INDO-US Research Fellowship Award 2012 (Awarded by INDO-US Science & Technology Forum) 
    • SERC Young Scientist Project Award 2012  (Under Department of Science &Technology Fast Track Scheme)
    • INSA Visiting Fellowship -2012
    • IASc-INSA-NASI Summer Research Fellowship – 2010

     

    Ph.D. Positions:


    Areas: Integro-Differential Equations; Numerical Methods for Fractional PDEs & Image Processing 


    Students are required to have a good understanding of the topic with good knowledge of the Functional Analysis. Studnets interested in Numerical work must have strong background in Numeircal Analysis with good programming skills in Matlab/ Mathematica. Students interested to work on Image processing are required to have knowledge of image processing and programming skills in Matlab.

    Postdoctoral Positions:

    Interested candidates are encouraged to apply for the post doctoral fellowships (NBHM, SERB-NPDF).