- Dynamic equation on time scale
- Differential equation (ODE)
- Non-additive measure theory
Experience top of the world living and learning at SRM University-AP
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SRM University, Andhra Pradesh
Neerukonda, Mangalagiri Mandal, Guntur District, Mangalagiri, Andhra Pradesh 522240
- 2021 - 2023 | Postdoctoral Fellow – Umea University, Sweden
- 2020 - 2020 | Assistant Professor (ad hoc)-Rajdhani College, University of Delhi
- 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.
- 2014 – JRF (Junior Research Fellow) – CSIR-UGC
- 2017 – SRF (Senior Research Fellow) – CSIR-UGC
- 2017– Best Presentation Award – SRM Chennai
- International Society of Difference Equations
- 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.
- E-mail id: shekharsingh.n@srmap.edu.in