rkpandey.mat's picture
Dr. Rajesh Kumar Pandey
Associate Professor
Department of Mathematical Sciences,IIT BHU.
rkpandey.mat@iitbhu.ac.in
9453897736
Area of Interest: 
Integral Equations; Spectral Methods; Wavelets; Fractional Derivatives; Image Processing

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.

Current Position:

  • Associate Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi:  July 19, 2017-till date.

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

  • Associate Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi:  July 19, 2017-till date.
  • 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 from: 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
  • Human Values

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
  • Singular Integral Equations
  • Spectral Methods; Wavelet Methods
  • Fractional Derivatives and Its Applications
  • Image Processing. 

Journal Publications: 

 Integral Equations: 

  • 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.
  • S. Sharma, R. K. Pandey, Kamlesh Kumar, Collocation method with convergence for generalized fractional integro-differential equationsJournal of Computational and Applied Mathematics, Accepted 2018 
  • S. Sharma, R. K. Pandey, K. Kumar, Galerkin and Collocation Methods for Weakly Singular Fractional Integro-differential EquationsIranian 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 EquationsInternational Journal of Applied and Computational Mathematics  Accepted 2018
  • K. Kumar, R. K. Pandey, S. Sharma, Approximations of Fractional Integrals and Caputo Derivatives with Application in Solving Abel’s Integral EquationsJournal 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 equationsJournal 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-OperatorASME 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 polynomialsApplied 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 Communications179 (2008) 424-429.                                                                                              
  • V. K. Singh, R. K. Pandey, O. P. Singh, New stable numerical solutions of  singular integral equations of Abel type by using normalized Bernstein  polynomials, Applied  Mathematical  Sciences Vol. 3 No. 5 (2008)441-455.                  

Image Processing:

  • 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 woodResearch 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 Algorithms11(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.
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 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 the student
Thesis Title/Proposed Area of research
Status
Current Position
Dr. Koushlendra Kumar Singh
Chebyshev Polynomial Based Approximation of an Efficient Fractional Order Mask for Different Image Processing Applications
Awarded 2016
Assistant Professor in Computer Science & Engg., NIT Jamshedpur
Dr. Harendra Singh
Weak Asymptotic Approach To Conservation Laws and Fractional Partial Differential Equations
Awarded 2016
Assistant Professor in Mathematics at Ghazipur PG College, Ghazipur UP 
Kamlesh Kumar
Numerical Approximations of Fractional Derivatives with Applications
Submitted Aug 2018
 
Dr. Shiva Sharma
Projection Approximation For Weakly Singular Integral and Integro-Differential Equations
Awarded Dec. 2018
 
Ashan Gupta
Integral Equations
Ongoing (On Leave)
 
Anil Kumar Shukla
Application of Fractional Derivatives in Image Processing
In Progress (July 2016)
 
Swati Yadav
Numerical Schemes for Some Fractional Partial Differential Equations
In Progress (July 2016)
 
Prashant Kumar Pandey
Fractional Differential Equations
In Progress (July 2017)
 

 

  • Member, DUGC, Mathematical Sciences, IIT(BHU) Varanasi for 2018-19.
  • 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.
  • Member, Faculty Forum IIT (BHU) Varanasi 2017-18.
  • Admin. Warden, Dr. S. Ramanujan Hostel, Indian Institute of Technology (BHU) Varanasi from May 30, 2018-till date.
  • 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 from March 2010 – till date.

Conference Workshop Organized

  • 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

  • Indian Mathematical Society (Life Member)
  • International Association of Engineers (IAENG)

Visit Abroad / Lectures Delivered

  • 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: Integral Equations; Integro-Differential Equations; 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).  

JRF Position (01):  
Interested candidates may send their CV for One JRF position in the SERB sanctioned research project entitled "Approximation Methods For Problems In Fractional Calculus Of Variations". The project is sanctioned for three years (2019-2022). For more details about recruitment, kindly send me an email on   rkpandey.mat@iitbhu.ac.in