Assistant Professor

Dr Shekhar Singh Negi

Department of Mathematics

Interests

  • Dynamic equation on time scale
  • Differential equation (ODE)
  • Non-additive measure theory

Faculty Details

Education

2011

Zakir Husain Delhi College,
University of Delhi

BSc

2013

Zakir Husain Delhi College,
University of Delhi

MSc

2020

Indian Institute of Technology Mandi
PhD

Professional Service

  • 2021 - 2023 | Postdoctoral Fellow – Umea University, Sweden
  • 2020 - 2020 | Assistant Professor (ad hoc)-Rajdhani College, University of Delhi

Research Interest

  • 1. The study of dynamic equations on time scales is an area of mathematics that deals with the analysis and solutions of differential equations and difference equations on general time scales. A time scale is a general framework that unifies continuous and discrete dynamics, allowing for a unified treatment of differential and difference equations.
  • 2. Non-additive measure theory, also known as non-additive integration theory or set-valued measure theory, is a branch of mathematics that deals with measures that do not satisfy the additively property. In traditional measure theory, measures assign values to sets in a way that is additive, meaning that the measure of the union of disjoint sets is equal to the sum of their individual measures. Non-additive measures generalize this concept by allowing for more flexible and versatile assignment of values to sets.
  • I am currently working on derivative of function with respect to the non-additive measure, more precisely, a distorted Lebesgue measure, called Sugeno derivative. The Sugeno derivative, also known as the Choquet derivative or fuzzy derivative, is a concept used in fuzzy set theory to define a derivative-like operator for fuzzy functions. It extends the notion of differentiation from classical calculus to fuzzy sets and allows for the analysis and modelling of fuzzy systems.

Awards & Fellowships

  • 2014 – JRF (Junior Research Fellow) – CSIR-UGC
  • 2017 – SRF (Senior Research Fellow) – CSIR-UGC
  • 2017– Best Presentation Award – SRM Chennai

Memberships

  • International Society of Difference Equations

Publications

  • Negi, S.S. and Torra, V., 2024. A note on Sugeno exponential function with respect to distortion. Applied Mathematics and Computation, 470, p.128586.
  • Grace, Said R., Syed Abbas, and Negi, S.S.. "Study of Oscillation Criteria of Odd-Order Differential Equations with Mixed Neutral Terms. Mathematica Slovaca, 73(5) (2023): 1231-1242.
  • Study of Oscillation Criteria of Odd-order Differential Equations With Mixed Neutral Terms- Said R. Grace, Syed Abbas, Negi, S. S., Mathematica Slovaca, Accepted 2023.
  •  Delta-Choquet integral on time scales with applications- Negi, S. S., Torra, V.- Chaos, Solitons Fractals, 157, p.111969, (2022).
  •  Existence and uniqueness of solutions of differential equations with respect to non-additive measures- Negi, S. S., V. Torra, Math. Methods Appl. Sci., 1-19 (2022).
  •  Oscillation theorems for second-order delay dynamic equation with super-linear neutral term- Said R. Grace, Negi, S. S., Abbas, S., Applied Mathematics and Computation, 412, 126576, (2022).
  • A generalized delta derivative on time scale with applications- Negi, S. S., Abbas, S., Malik, M., Math. Methods Appl. Sci., 43(15), 9046-9079, (2020).
  • Oscillation for a nonlinear neutral dynamic equation on time scale with variable exponents- Negi, S. S., Abbas, S., Malik, M., Math. Methods Appl. Sci., 42(12), 4146-4169, (2019).
  • Oscillation Criteria of Special Type Second-Order Delayed Dynamic Equations on Time Scales- Negi, S. S., Abbas, S., Malik, M., Xia. Y. H., Math. Sci., 12(1), 25 -39, (2018).
  • Study for a new oscillation criteria of a p-laplacian dynamic equation on time scale- Negi, S. S., Abbas, S., Malik, M., Said R. Grace, Rocky Mountain J. Math., 50(2), 659-670, (2020).
  • Periodic solutions of the N-preys and M-predators model with variable rates on time scale order non-linear dynamic equation on time scales- Negi, S. S., Abbas, S., Malik, M., Indian J. Pure Appl. Math., 51, 945-967, (2020).
  •  Oscillation Criteria of Singular Initial-Value Problem for Second Order Non Linear Dynamic Equation on Time Scales- Negi, S. S., Abbas, S., Malik, M., Nonauton. Dyn. Syst., 5(1), 102-112, (2018).
  • Oscillation of second-order non-canonical non-linear dynamic equations with a sub-linear neutral term- Abbas, S., Grace, S.R., Graef, J.R., Negi, S. S., Differential Equations and Dynamical Systems, Differ. Equ. Dyn. Syst., 1-11, (2022).
  • Oscillation Criteria of Second- Order Nonlinear Dynamic Equations with Integro Forcing Term on Time Scales- Negi, S. S., Abbas, S., Malik, M., Bulletin of SUSU. MMCS., 10(1), 35-47, (2017).

International Conferences

  • 1. Oscillation Criteria for the Higher-order Nonlinear Dynamic Equation on Time Scales with Variable Coefficients- Negi, S. S., Abbas, S., Malik, M., International congress of Mathematician, 2018.
  • 2. Conference on "International Conference on Differential Equations and Control Problems: Modelling, Analysis and Computations (ICDECP19)" organized by the School of Basic Sciences, IIT Mandi, India during June 17-19, 2018

Book Chapters

  • Oscillation of the Class of Second Order Nonlinear Dynamic Equation on Time Scales with Variable Coefficients- Negi, S. S., Abbas, S., Malik, M., Mathematical Modelling and Computational Tools Publisher: Springer Singapore, 2020. DOI: 10.1007/978-981-15-3615-130

Survey Papers

  • Abbas, S., Negi, S. S., Grace, S.R., Agarwal, R.P., Wang, C.: Survey on Qualitative Theory of Dynamic Equations on Time Scale, Memoirs on Differential Equations and Mathematical Physics,84, pp.1-67, (2021).

Workshops

  • 1. Workshop on "Science Academies Lecture Workshop on Essence of Partial Differential Equation" organized by the School of Basic Sciences, IIT Mandi, India during April 02-04, 2018.
  • 2. Advance Level Training program on "Advance Mathematics for Researchers in Engineering Field" organized by the School of Basic Sciences, IIT Mandi, India during March 24-28, 2017.
  • 3. National Level Training program on differential Equations with Applications in Engineering" organized by the School of Basic Sciences, IIT Mandi, India during July 01-08, 2016.
  • 4. Workshop on “Controllability of Heat and Wave equations" organized by the School of Basic Sciences, IIT Mandi, India during November 16-20, 2015.

Contact Details

  • E-mail id: shekharsingh.n@srmap.edu.in
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