- About me
- Teaching
- Research
- Publications
- Projects
- Research Guidance
- Administration
- Activities (Conferences/Workshops)
- Awards
- Opportunities
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
- Integro-Differential Equations
- Spectral Methods; Wavelet Methods
- Fractional Derivatives and Its Applications
- Image Processing.
Journal Publications:
Integral and Integro-Differential Equations:
- K Kumar, RK 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.
- 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 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, 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 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.
- 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 Student | Thesis Title / Topic 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 Equations | Awarded 2016 |
Dr. Kamlesh Kumar (Assistant Professor in Mathematics at Manav Rachna University Faridabad, Haryana) |
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 Dec. 2018 |
Dr. Anil Kumar Shukla | Newly Introduced Fractional Filters for Image Processing Applications | Awarded Jan. 2021 |
Dr. Swati Yadav | Numerical Schemes for Some Fractional Partial Differential Equations | Awarded March 2021 |
Prashant Kumar Pandey | Approximation Methods for Fractional Sturm-Liouville Problems | Thesis Submitted April19 2022 |
Sandeep Kumar | Integro-Differntial Equations | In Progress (July 2018) |
Deeksha Singh | Numerical Schemes for Fractional PDEs | In Progress (Dec. 2018) |
Farheen Sultana | High Order Schemes for Fractional PDEs | In Progress (Dec. 2018) |
- Convener, TPO, Mathematical Sciences, IIT(BHU) Varanasi for 2021-22.
- Member, DPGC, Mathematical Sciences, IIT (BHU) Varanasi for year 2020-21.
- Convener, DPGC, Mathematical Sciences, IIT (BHU) Varanasi for year 2019-20.
- Member, DUGC, Mathematical Sciences, IIT(BHU) Varanasi for 2018-19, 2021-22.
- 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-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.
Editorial Assignments
- 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
- 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
- Treasurer, Mathematics and Computing Society, Mathematical Sciences, IIT (BHU) Varanasi
- Life Member, Indian Mathematical Society
- Life Member, Ramanujan Mathematical Society
- 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).
- 5^{th} 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 21^{st} 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 : NIL