Assistant Professor (Grade-II)

Manish.bansal@mail.jiit.ac.in

#### EDUCATION

- Ph.D. (MNIT, Jaipur)
- M.Sc. Tech(Central University of Rajasthan, Ajmer)

#### Work Experience

**November 2021 to ongoing**: Assistant Professor, Department of Mathematics, Jaypee Institute of Information Technology, Sector-62, Noida, Uttar Pradesh, India.**January 2018 to September 2021**: Assistant Professor, Department of Applied Sciences, Govt. Engineering College, Banswara.**January 2017 to December 2017**: Assistant Professor, Department of Mathematics, Malaviya National Institute of Technology, Jaipur.**January 2015 to December 2016**: Senior Research Fellow (Ph.D. Student), Department of Mathematics, Malaviya National Institute of Technology, Jaipur.**January 2013 to December 2014**: Junior Research Fellow (Ph.D. Student), Department of Mathematics, Malaviya National Institute of Technology, Jaipur.

#### Interest Area(s)

- Fractional Calculus, Special Functions.

#### RESEARCH PROJECTS

- Title of Project: A study of Incomplete Special Functions and their applications
- Funding Agency: TEQIP-III and sanctioned by NPIU(A unit of MHRD, GOI)
- Duration of Project: June 2019 to September 2021
- Principal Investigator: Dr. Manish Kumar Bansal
- Total Amount of Project: 7.35 lacs
- Project ID: 1-5730065311
- Status: Completed

#### Publications

**International Journals**

- Harjule, P., Bansal, M.K. and Araci, S. “An Investigation of Incomplete H-Functions associated with some fractional integral operators”, FILOMAT, (in press)(SCI, IF-0.844).
- Jolly, N. and Bansal, M.K. Several inequalities involving the generalized multi-index Mittag-Leffler functions, Palestine journal of mathematics, (in press). (SCOPUS).
- Bansal, M.K., Shivlal, Kumar, D., Kumar, S. and Singh, J. “Fractional Differential Equation pertaining to a Integral operator involving the family of Incomplete H-functions in the kernel”, Math Meth Appl Sci.(Willey) (in press). (SCI, IF-2.321).
- Bansal, M.K., Harjule, P. and Kumar, D. “Fractional Differential Equations associated with M-S-M fractional integral operator in Fp,ν space”, Thai Journal of Mathematics (in press). (SCOPUS).
- Bansal, M.K. and Kumar, D. “on a family of the incomplete H-functions and associated integral transforms”, Journal of applied analysis, 27(1), 143-152, (2021). (SCOPUS).Bansal, M.K., Kumar, D., Singh, J., Tassaddiq A. and Nisar, K.S. “Some New Results for the Srivastava-Luo-Raina M-Transform Pertaining to the Incomplete H-Functions”, AIMS-Mathematics, 5(1), 717-722, (2020). (SCI, IF-1.427).
- Bansal, M.K. and Kumar, D. “On the integral operators pertaining to a family of incomplete I−functions”, AIMS-Mathematics, 5(2), 1247-1259, (2020). (SCI, IF-1.427).
- Singh, J., Kumar, D. and Bansal, M.K. “Solution of Nonlinear Differential Equation And Special Functions”, Math Meth Appl Sci.(Willey), 43(5), 2106-2116, (2020).(SCI, IF-2.321).
- Bansal, M.K., Kumar, D., Nisar, K.S. and Singh, J. “Certain fractional calculus and integral transform results of incomplete ℵ-functions with applications”, Math Meth Appl Sci.(Willey), 43(8), 5602-5614, (2020). (SCI, IF-2.321).
- Bansal, M.K., Kumar, D., Harjule, P. and Singh, J. “Fractional Kinetic Equations Associated with Incomplete I-Functions”, Fractal and Fractional, 4(2), 19; (2020).(SCI, IF-3.313 ).
- Bansal, M.K., Kumar, D., Singh, J. and Nisar, K.S. “On the Solutions of a Class of Integral Equations Pertaining to Incomplete H-Function and Incomplete H-Function”, Mathematics, 8(5), 819, (2020). (SCI, IF-2.258).
- Harjule, P. and Bansal, M.K. “Fractional Order Models for Viscoelasticity in Lung Tissues with Power, Exponential and Mittag–Leffler Memories”, Int. J. Appl. Comput. Math, 6(4), Art. 119, (2020). (SCOPUS).
- Jolly, N., Bansal, M.K., Kumar, D. and Singh, J. “Certain Mathieu-type Series Pertaining to Incomplete H-Functions”, Applications and Applied Mathematics(AAM), 15(3), 1-14, (2020).(ESCI, WoS)
- Purohit, S.D., Jolly, N., Bansal, M.K., Singh, J. and Kumar, D., “Chebyshev Type Inequalities Involving the Fractional Integral Operator Containing Multi-Index Mittag-Leffler Function in the Kernel”, Applications and Applied Mathematics(AAM), 15(3), 29-38, (2020).(ESCI, WoS)
- Bansal, M.K., Kumar, D., Singh, J. and Nisar, K.S., “Finite and infinite integral Formulas involving the family of Incomplete H-functions”, Applications and Applied Mathematics(AAM), 15(3), 15-28, (2020).(ESCI, WoS)
- Kumar, D., Bansal, M.K., Nisar, K.S. and Singh, J. “Mathematical Modelling of Internal Blood Pressure Involving Incomplete H−functions”, J. Interdiscip. Math., 22(7), 1213-1221, (2019) (ESCI, WoS).
- Bansal, M.K., Kumar, D., Nisar, K.S. and Singh, J. “Application of incomplete H−functions in determination of Lambert’s Law”, J. Interdiscip. Math., 22(7), 1205-1212, (2019) (ESCI, WoS).
- Bansal, M.K., Jolly, N., Jain, R. and Kumar, D. “An Integral Operator Involving Generalized Mittag-Leffler Function and Associated Fractional Calculus Results”, The Journal of Analysis, 27(3),727-740, (2019). (SCOPUS).
- Srivastava, H.M., Jolly, N., Bansal, M.K. and Jain, R. “A New Integral Transform Associated with The λ-Extended Hurwitz-Lerch Zeta Function, RACSAM, 113(3), 1679-1692, (2019). (SCI, IF-2.169).
- Bansal, M.K., Kumar, D. and Jain, R. “A Study of Marichev-Saigo-Maeda Fractional Integral Operators Associated with S-Generalized Gauss Hypergeometric Function”, Kyungpook Math. J., 59(3), 433-443, (2019). (ESCI,SCOPUS & WoS).
- Bansal, M.K., Kumar, D. and Jain, R. “Interrelationships Between Marichev-Saigo-Maeda Fractional Integral Operators, the Laplace Transform and the H¯ -Function, Int. J. Appl. Comput. Math, 5(4), Art. 103, (2019). (SCOPUS).
- Bansal, M.K. and Choi, J. “A Note on Pathway Fractional Integral Formulas Associated with the Incomplete H−Functions”, Int. J. Appl. Comput. Math, 5(5), Art. 133, (2019). (SCOPUS).
- 23. Bansal, M.K., Kumar, D., Khan, I. Singh, J. and Nisar, K.S. “Certain Unified Integrals Associated with Product of M−Series and Incomplete H−functions”, Mathematics, 7(12), 1191, (2019). (SCI, IF-2.258).
- Bansal, M.K., Harjule, P., Choi, J., Mubeen, S. and Kumar, D. “Certain Formulas Involving A Multi-Index Mittag-Leffler Function”, East Asian Math. J., The Youngnam Mathematical Society, 35(1), 23-30, (2019).
- Srivastava, H.M., Bansal, M.K. and Harjule, P. “A Study of Fractional Integral Operators Involving A Certain Generalized Multi-Index Mittag-Leffler Function, Math Meth Appl Sci.(Wiley), 41(16), 6108-6121, (2018). (SCI, IF-2.321).
- Bansal, M.K. and Jolly, N. Tur´an-Type, Lazarevi´c and Wilker-Type Inequalities for the Generalized Wright Functions, Journal of Advanced Research in Dynamical and Control System, 10(9), 2529-2535, (2018). (SCOPUS).
- Bansal, M.K. and Jain, R. “A Study of Unified Fractional Integral Operators Involving S-Generalized Gauss’s Hypergeometric Function as It’s Kernel”, Palestine Journal of Mathematics, 6(1), 142–152, (2017). (SCOPUS).
- Bansal, M.K. and Jain, R. “Analytical Solution of Bagley Torvik Equation by Generalized Differential Transform”, International Journal of Pure and Applied Mathematics, 110(2), 265-273, (2016). (SCOPUS).
- Bansal, M.K. and Jain, R. “Application of Generalized Differential Transform Method to Fractional Order Riccati Differential Equation and Numerical Result”, International Journal of Pure and Applied Mathematics, 99(3), 355-366, (2015). (SCOPUS).
- Srivastava, H.M., Jain, R. Bansal, M.K. “A study of the S-generalized Gauss hypergeometric function and its associated integral transforms”, Turkish Journal of Analysis and Number Theory, 3(5), 116-119, (2015).

**National Journals**

- Harjule, P., Bansal, M.K. and Jain, R. “A General Voltera-type integral equation associated with an integral operator with the H-Function in the kernel”, Global Journal of Pure and Applied Mathematics, 13(9), 6973-6978, (2017).
- Bansal, M.K. and Jain, R. “Certain new results of the S-generalized Gauss hypergeometric function transform”, South East Asian J. of Math. & Math.Sci., 12(2), 115-124, (2016). (UGC).
- Bansal, M.K. and Jain, R. “A study of finite integral involving generalized form of the Astrophysical Thermonuclear function”, Journal of Rajasthan Academy of Physical Sciences, 14(1),
- 51-55, (2015). (UGC).
- Bansal, M.K. and Jain, R. “Composition formulae for unified fractional integral operators”, European Journal of Advances in Engineering and Technology. 3(4), 1-6, (2016).
- Bansal, M.K. and Jain, R. “Application of generalized differential transform method to fractional Relaxation Oscillation equation”, Antarctica Journal of Mathematics, 12(1), 85-95, (2015).
- Bansal, M.K. and Jain, R. “On unified finite integrals involving I3 function, generalized Mittag-Leffler function and Appell polynomials”, The Journal of the Indian Academy of Mathematics, 36(2), 211-219, (2014)

**International/National Conferences**

Attended/Abstract Published

- Presented a paper entitled “Image formulae for the M-S-M fractional integral operators associated with the multi-index Mittag-Leffler functions” in the ICMMAA-2019 at JECRC University, Jaipur (Raj), India during Aug 8-10,2019.
- Presented a paper entitled “Application of generalized differential transform method to fractional order Riccati differential equation and numerical result” in the National Conference on Mathematical Analysis and Computation (NCMAC)-2015 at the Malaviya National Institute of Technology Jaipur-302017 (Raj), India during Feb 20-21, 2015.
- Presented a paper entitled “Analytical solution of Bagley Torvik equation by generalized differential transform” in the International Conference on Special Functions and its Applications (ICSFA)-2014 at Thapar University, Patiala-147004 (Punjab), India, during Oct 16-18, 2014.
- Presented a paper entitled “Application of generalized differential transform method to fractional Relaxation Oscillation equation” in the Computatia-IV at the Vivekanand Institute of Technology, Jaipur (Raj), India, during Nov 25-26, 2014.
- Presented a paper entitled “A study of finite integral involving generalized form of the astrophysical thermonuclear function” in the International Conference on Special Functions and its Applications (ICSFA)-2013 at Malaviya National Institute of Technology Jaipur-302017 (Raj.), India during Dec 13-15, 2013.

#### ORGANISED SHORT TERM COURSE /WORKSHOP/SEMINAR/CONFERENCE

- Two days TEQIP-III Sponsored Workshop on Latex: A Tool for Manuscript Writing and Typesetting at Govt. Engineering College, Banswara, India during April 9-10, 2018.
- One week TEQIP-III Sponsored STC on Latex & Mathematica for Beginners at Govt. Engineering College, Banswara, India during August 27-31, 2019.
- Three days TEQIP-III Sponsored Online Workshop on Research Methodology in higher Education at Govt. Engineering College, Banswara, India during Sept 03-05, 2020.
- One week TEQIP-III Sponsored Online STTP on Higher Engineering Mathematics at Govt. Engineering College, Banswara, India during October 05-10, 2020

#### PARTICIPATED IN SHORT TERM COURSE /WORKSHOP/SEMINAR/CONFERENCE

- One week Short Term Course on Advanced Pedagogies: Active Learning and Digital Tools at IIT Delhi, India during June 17-21,2019.
- Two week Faculty Development Programme on Advanced Optimization Techinques at Malaviya National Institute of Technology Jaipur, India during October 12-21, 2018.
- One week Faculty Induction Program at IIT Gandhinagar, India during Jan 29-Feb 02, 2018.
- One week Short Term Course on Modeling & Simulation Tools at Malaviya National Institute of Technology Jaipur, India during July 03-07, 2017.
- Two Days Workshop on LATEX: for Research at Malaviya National Institute of Technology Jaipur, India during July 23-24, 2016.
- One week Short Term Course on MATLAB, A Tool in Research at Malaviya National Institute of Technology Jaipur, India during December 24-28, 2015.
- One week Short Term Course on Mathematical Modeling, MATLAB Programming and their Applications in Engineering and Sciences at Malaviya National Institute of Technology Jaipur, India during January 19-23, 2015.
- One Week National Workshop on LATEX and MATLAB FOR BEGINNERS at Birla Institute of Technology & Science Pilani, India during December 24-28, 2014.
- One week Short Term Course on Analysis and Applications at Malaviya National Institute of Technology Jaipur, India during Nov 10-14, 2014.
- Two Days 2ndNational Workshop on Scientific Computational Techniques at Manipal University Jaipur, India during December 18-19, 2014.
- Two days 4th National Conference on Computational and Mathematical Sciences : COMPUTATIA-IV at Vivekananda Institute of Technology, Jaipur, India during Nov 25-26, 2014.
- Two days 4th National Conference on Computational and Mathematical Sciences : COMPUTATIA-2012 at Vivekananda Institute of Technology, Jaipur, India during Jan 28-29, 2012.
- Two days National Seminar on Advances in Complex Analysis and Special Functions at Central University of Rajasthan, Ajmer, India during March 12-13, 2011.
- Two days National Conference of Rajasthan Ganita Parishad on Recent Trends in Mathematics & Actuarial Sciences at Central University of Rajasthan, Ajmer, India during Feb 20-21, 2010.
- One week Short Term Course on Advanced Computing and Analysis Techniques in Physics Research at Laxmi Niwas Mittal Institute of Information Technology Jaipur, India during Feb 22-27, 2010.

#### NPTEL/MOOC COURSE

- Completed 12 week NPTEL course on Transform Calculus and Its Applications in Differential Eqations securing 90% Marks(Gold Certified-in Top 5%) conducted by IIT Kharagpur during Jan-April, 2019.
- Completed 12 week NPTEL course on Mathematical Methods and Its Applications securing 80% Marks(Elite Certified) conducted by IIT Roorkee during Jan-April, 2019.
- Completed 12 week NPTEL course on Advanced Engineering Mathematics securing 75% Marks(Elite Certified) conducted by IIT Roorkee during Jan-April, 2019.

#### QUALIFIED NATIONAL LEVEL TESTS

- GATE in Mathematics, All India Rank 181, Year 2012.
- JAM in Mathematics, All India Rank 183, Year 2010.
- CUCET in Mathematics, All India Rank 02, Year 2009.

#### REVIEWER

- American Mathematical Review.
- International journal of Applied and Computational Mathematics, Springer.
- Thai Journal of Mathematics.
- International Journal of Differential Equations, Hindawi.
- Mathematics in Engineering, Science and Aerospace (MESA).
- Advances in Difference Equations, Springer.
- Moroccan Journal of Pure and Applied Analysis.
- Advances and Applications in Mathematical Sciences.
- Afrika Matematika, Springer.
- TWMS Journal of Applied and Engineering Mathematics.
- Symmetry, MDPI.

#### Membership

- International Conference on Special Functions and its Applications (ICSFA), Life Member (1113).
- International Association of Engineers, Life Member (210594).