Dr. Rajeev

Associate Professor

Department of Mathematical Sciences,IIT BHU.

rajeev.apm@iitbhu.ac.in

+91 9451941396

Area of Interest:

Mathematical Modelling, Moving Boundary Problems

- Ph. D. in Applied Mathematics, IIT (BHU) in 2009
- M. Sc. in Mathematics, Banaras Hindu University (2004)
- B. Sc. in Mathematics (Honours), Banaras Hindu University (2002)

**Associate Professor**in Department of Mathematical Sciences,**Assistant Professor**(Mathematics) in the Department of Mathematical Sciences, IIT (BHU), Varanasi from 30-10-2007 to July 18, 2017.**Assistant Professor**(Mathematics) in the Department/ Faculty of Commerce, BHU, Varanasi from 10-07-2006 to 30-10-2007.

__Courses Taught at Indian Institute of Technology (BHU)__

**Engineering Mathematics I****Mathematical Methods****Numerical Techniques****Finite Element Method**

**Rajeev**, K.N. Rai, S. Das, Numerical solution of a moving-boundary problem with variable latent heat,*Int. J. Heat and Mass Transfer*52 (2009) 1913–1917.**Rajeev**, K. N. Rai, and S. Das, Solution of one-dimensional moving boundary problem with periodic boundary condition by variational iteration method,*Thermal Science*, 13 (2009), pp. 199-204.- S. Das, P.K. Gupta and
**Rajeev**, A fractional predator- prey model and its solution,*Int. J. Non-linear Sci. and Numerical Simulation,*10 (2009), pp. 873-876. **Rajeev**and S Das, A numerical study for inward solidification of a liquid contain in cylindrical and spherical vessel,*Thermal Science*, 14 (2010), pp. 365-372.- S. Das,
**Rajeev**, Solution of fractional diffusion equation with a moving boundary condition by variational iteration method and Adomian decomposition method, Z. Naturforsch**.**65a (2010) 793–799. - S. Das and
**Rajeev**, An approximate analytical solution of one-dimensional phase change problems in a finite domain,*Applied Mathematics and Computation*, 217 (2011), 6040–6046. **Rajeev**, M. S. Kushwaha, Homotopy perturbation method for a limit case Stefan problem governed by fractional diffusion equation,*Applied Math. Modell.*, 37 (2013), pp. 3589–3599.**Rajeev,**M S Kushwaha, Ajay Kumar, An approximate solution to a moving boundary problem with space–time fractional derivative in fluvio-deltaic sedimentation process,*Ain Shams Engg. J (Elsevier)*4 (2013), pp. 889–895.**Rajeev**, Homotopy perturbation method for a Stefan problem with variable latent heat,*Thermal Science*18 (2014), pp. 391-398.**Rajeev**, M.S. Kushwaha, A.K. Singh, A study of a Stefan problem governed with space–time fractional derivatives,*Journal of Heat and Mass Transfer Research,*3 (2016), 145-151.**Rajeev**and A.K. Singh, Homotopy analysis method for a fractional Stefan problem,*Nonlinear Sci. Lett. A,*8(2017) 50-59.**Rajeev**and A.K. Singh, A wavelet based approach to a moving boundary problem,*Nonlinear Sci. Lett. A, Vol.*8, (2017), (3), pp.294-302.- A K Singh, A Kumar,
**Rajeev**, A Stefan problem with variable thermal coefficients and moving phase change material,*Journal of King Saud University – Science*, 31, (4), 2019, pp 1064-1069. - A. K. Singh, A. Kumar and
**Rajeev,**Exact and approximate solutions of a phase change problem with moving phase change material and variable thermal coefficients.*J. King Saud Univ. Sci.*, 31 (4),**2019, pp**1318-1325. - Ajay Kumar, A K Singh,
**Rajeev**, A phase change problem including space-dependent latent heat and periodic heat flux,*Nonlinear Dynamics and Systems Theory*, 19 (1-SI) (2019) 178–185. - K. D. Dwivedi,
**Rajeev**and S. Das, Fibonacci Collocation Method to Solve Two-dimensional Nonlinear Fractional Order Advection-Reaction Diffusion Equation,*Special Topics & Reviews in Porous Media*, 10 (6), 2019, pp.**569-584.** **Rajeev**and Mohan Singh Kushwaha, Comparison between Adomian decomposition method and optimal homotopy asymptotic method for a two moving boundaries problem,*Differential Equations and Dynamical Systems (Springer)**,***28**, (2020), pp. 431–446.- A. Kumar, A.K. Singh,
**Rajeev**, A Stefan problem with temperature and time dependent thermal,*Journal of King Saud University*– Science, 32 (1), 2020, pp 97-101. - KD Dwivedi,
**Rajeev**, S Das, D Baleanu, Numerical Solution of Nonlinear Space–Time Fractional-Order Advection–Reaction–Diffusion Equation, Journal of*Computational and Nonlinear Dynamics*(Transactions of the ASME), 15 (6), 2020, 061005. - A. Kumar, A.K. Singh,
**Rajeev**, A moving boundary problem with variable specific heat and thermal conductivity,*Journal of King Saud University – Science*, 32 (1), 2020, pp. 384-389. - Lipi Jain, Abhishek Kumar,
**Rajeev**, A numerical study of a moving boundary problem with mixed boundary condition and variable thermal coefficients,*Computational Thermal Sciences*, 12(3), 2020, pp. 249–260. - Abhishek Kumar,
**Rajeev**, A Stefan problem with moving phase change material, variable thermal conductivity and periodic boundary condition,*Applied Mathematics and Computation*, 386 (2020) 125490 - A. Kumar, A.K. Singh,
**Rajeev**, A freezing problem with varying thermal coefficients and convective boundary condition.*Int. J. Appl. Comput. Math.,*6 (5) (2020), Article number: 148. - Abhishek Kumar,
**Rajeev**, A moving boundary problem with space-fractional diffusion logistic population model and density-dependent dispersal rate,*Applied Mathematical Modelling*, 88 (2020), pp 951–965. - Mahesh Kumar, K.N. Rai,
**Rajeev**, A study of fractional order dual-phase-lag bioheat transfer model,*Journal of Thermal Biology*, 93 (2020) 102661. - KD Dwivedi,
**Rajeev**, S. Das, J F Gomez-Aguilar, Finite difference/collocation method to solve multi term variable-order fractional reaction–advection–diffusion equation in heterogeneous medium.*Numerical Methods Partial Differential Eq.*2020; 1–15, https://doi.org/10.1002/num.22648. - Kumar, M., Rai, K.N. &
**Rajeev**, Analysis of DPL Bioheat Transfer Model During Thermal Treatment.*Int. J. Appl. Comput. Math***7, 44**(2021). https://doi.org/10.1007/s40819-021-00976-w - M Singh, S Das,
**Rajeev**, EM Craciun, Numerical solution of two-dimensional nonlinear fractional order reaction-advection-diffusion equation by using collocation method,*An. St. Univ. Ovidius Constanta*29 (2), 211-230, 2021. - Dwivedi, K.D., Rajeev Numerical Solution of Fractional Order Advection Reaction Diffusion Equation with Fibonacci Neural Network.
*Neural Process Letter***53,**2687–2699 (2021). https://doi.org/10.1007/s11063-021-10513-x - A. Kumar, V. K. Yadav, S. Das and
**Rajeev**, "Global Exponential Stability of Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Network With Time-Varying Delays," in*IEEE Control Systems Letters*, vol. 6, pp. 325-330, 2022, doi: 10.1109/LCSYS.2021.3073962. - K D Dwivedi, S Das,
**Rajeev**, D Baleanu, Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method,*International Journal of Nonlinear Sciences and Numerical Simulation*, 2021, https://doi.org/10.1515/ijnsns-2020-0112 - Ankit Kumar, S Das,
**Rajeev**, V.K. Yadav, Global exponential synchronization of complex-valued recurrent neural networks in presence of uncertainty along with time-varying bounded and unbounded delay terms,*Int. J. Dynam. Control*(2021). https://doi.org/10.1007/s40435-021-00838-9 - Ankit Kumar, S. Das, V.K. Yadav,
**Rajeev**, Jinde Cao and C Huang, Synchronizations of fuzzy cellular neural networks with proportional time-delay,*AIMS Mathematics*, 6(10),**2021**10620–10641. - Ankit Kumar, S. Das, Vijay K. Yadav,
**Rajeev**, Global quasi-synchronization of complex-valued recurrent neural networks with time-varying delay and interaction terms,*Chaos, Solitons & Fractals*, 152, 2021, 111323. - Abhishek Kumar,
**Rajeev,**Heat balance integral method for a time-fractional Stefan problem with Robin boundary condition and temperature-dependent thermal conductivity,*Computational Thermal Sciences*, 13 (6), 2021, 71–84.

**Ph.D. Supervision :**

- Mr. M. S. Kushwaha (Awarded in 2015)
- Mr. Ajay Kumar (Awarded in 2019)
- Mr. A.K. Singh (Awarded in 2019)
- Mr. Kushal Dhar Drivedi (Thesis submitted in 2021)
- Mr. Abhishek Kumar (Ongoing)
- Mr. Mahesh Kumar (Ongoing)
- Mr. Ankit Kumar (Ongoing)
- Mr. Manipal Singh (Ongoing)
- Ms Rashmi Sharma (Ongoing)
- Mr. Ankit Kumar (Ongoing)
- Ms Lipi Jain (Ongoing)

**M.Tech. Supervision :**

- Mr. Rahul Rajput (08412EN001), Awarded in 2013 (supervisor)
- Ms. Purnima Lodha (09412EN006), Awarded in 2014 (supervisor)
- Mr. Aditya Modi (09412EN008), Awarded in 2014 (supervisor)
- Mr. Naresh Kumar Raigar (10412EN014), Awarded in 2015 (supervisor)
- Mr. Shubham Agrawal (11412EN006), Awarded in 2016 (supervisor)
- Mr. Kethavath Janardhan (12412EN020) Awarded in 2017(supervisor)
- Mr. Mayank Aharwar (13123011), Awarded in 2018 (supervisor)
- Mr. Rishabh Dall (13123013), Awarded in 2018(supervisor)
- Mr. Ishkaran Mangat (14123021), Awarded in 2019 (supervisor)
- Mr. Arun Meena (13123003) Awarded in 2019 (co-supervisor)
- Mr. Rahul Maurya (13123012) Awarded in 2019 (co-supervisor)
- Mr. Khushal Patidar (15123007) Awarded in 2020(supervisor)
- Mr. Vaibhav Kumar Dixit (16123018) Awarded in 2021(supervisor)
- Mr. Anshuman Singh (16123006) Awarded in 2021(supervisor)

Activities:

**Treasurer**in**RTMMS-2010 (**a National conference from March 18 - 20, 2010).**Organizing Secretary and Treasurer**in**RTMMS-2011 (**a National conference from March 25 - 27, 2011**).****Organizing Secretary and Treasurer in MMCS-2012 (a**National Conference from March 23 - 25, 2012).**Course Coordinator of**AICTE sponsored QIP-Short Term Course on*Advanced Numerical Schemes**for Scientists & Engineers (ANSSE-19) during**Aug. 12-16, 2019.***Course Coordinator of a o**ne day workshop on “Study and Analysis of Mathematical Models of Moving Boundary Problems” sponsored by Science and Engineering Research Board (SERB), Govt. of India on August 17, 2019.**Chair a session**in 17th International Conference on Mathematical Sciences, Engineering and Applications (ICMSEA), July 4-5, 2015,**Singapore**.**Chair a session**in ICDECP19 , June 17-19, 2019 IIT Mandi.- Reviewer in reputed journals.

**paper presentation/invited talk/Lectures Delivered**

- National conference on recent trends in Mathematical Modeling and Simulation (
**RTMMS-2010**) organized by Dept. of Applied Mathematics, I.T., BHU, Varanasi, March 18-20, 2010.Topic: A numerical study for a Stefan problem subject to the periodic boundary conditions. - National Conference on Mathematical Modeling and Computer Simulation (
**MMCS-2011**) organized by Dept. of Applied Mathematics (Under SAP), I.T., BHU, Varanasi, March 25-27, 2011.**Topic:**A numerical approach for a moving boundary problem with time-dependent boundary conditions - National conference on Mathematical Modeling and Computer Simulation (
**MMCS-2012**) organized by Dept. of Applied Mathematics (Under SAP), Institute of Technology, BHU Varanasi, March 23-25, 2012.**Topic:**An approximate solution to a moving boundary problem in fluvio-deltaic sedimentation process. - A talk in International Conference on Recent Advances in Pure and Applied Mathematics
**,**ANTALYA,**TURKEY,**Nov 6-9, 2014**. Topic:**An approximate solution to a problem of two moving boundaries governed with fractional time derivative in drug release devices. - 17
^{th }International Conference on Mathematical sciences, Engineering and Applications (ICMSEA),**2015**,**Singapore,**July 4-5.Topic:A Numerical Solution Based On Operational Matrix of Differentiation of Shifted Second Kind Chebyshev Wavelets for a Stefan Problem. - 2
^{nd}International conference on Mathematical Techniques in Engineering Applications (**ICMTEA 2016**),**Dehradun**, Uttarakhand, April 29-30, 2016.Topic: Comparison between Adomian decomposition method and optimal homotopy asymptotic method for a two moving boundaries problem. - International Conference on Mathematical Modelling in Applied Sciences (ICMMAS’17) during July 24-28, 2017, in Peter the Great St. Petersburg Polytechnic University,
**Russia**. Topic: A numerical solution of a moving boundary problem. - International Conference on Applied and Computational Mathematics (ICACM-2018) during November 23-25, 2018, IIT Kharagpur.
**Topic:**A Spectral Collocation approach to a melting problem including variable thermal coefficients. - Invited talk in an
**International Conference ICDECP19**during June 17-19, 2019, IIT Mandi.**Topic:**A Finite element approach to a moving boundary problem with variable thermal conductivity. - Guest lecture in an AICTE sponsored QIP-Short Term Course on
*Advanced Numerical Schemes for Scientists & Engineers (ANSSE-19)*during - Guest lecture in
**a o**ne day workshop on “Study and Analysis of Mathematical Models of Moving Boundary Problems” sponsored by SERB, Govt. of India on August 17, 2019, in the Dept of Mathematical Sciences, IIT(BHU). - Invited talk in
**an International Conference on Computational Mathematics and its Applications (CMA 2019)CMA 2019**during Nov. 12-14, 2019, IIT Indore.**Topic:**A phase Change Problem with variable thermal conductivity by Spectral Collocation and spectral Tau methods.

- Warden of ASN Bose Hostel, IIT (BHU) Varanasi from 18/09/2012 to 29/05/2018.
- Admin Warden of ASN Bose Hostel, IIT (BHU) Varanasi from 30-05-2018 to 31-05-2021.
- Convener of the DUGC during 2017-18, Department of Mathematical Sciences, IIT(BHU) Varanasi.
- a member of the Departmental faculty Affairs committee (DFAC) for the session 2019-20.
- a member of BoG of Rajkiya Engineering College, Ambedkar Nagar (UP) from March 2019 till date.

1. A project of Science and Engineering Research Board (SERB) of the total cost of Rs. 2244000/- (Rs. Twenty Two Lakh Forty Four Thousand Only) for three years.

Project No.: R&D/SERB/Math/18-19/02 Project start date is 22-Feb-19

Topic: Study and Analysis of Mathematical Models of Moving Boundary Problems.