shekhar negi

About

I am currently working on the derivative of a function with respect to the non-additive measure, more precisely, a distorted Lebesgue measure, called the 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 modeling of fuzzy systems.

The Non-additive measure theory, also known as non-additive integration theory or set-valued measure theory, is a branch of mathematics dealing with measures that do not satisfy the additive property. In traditional measure theory, measures assign values to sets in an additive way, meaning that the measure of the union of disjoint sets is equal to the sum of their measures. Nonadditive measures generalize this concept by allowing for more flexible and versatile assignment of values to sets.

Before joining Umea University, Sweden as a postdoctoral fellow, I worked on dynamic equations on time scale theory. 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

Employment

• SRM University, Andhra Pradesh Assistant Professor (Grade-1)
  2023 - Present
• Umeå Universitet Postdoc Fellow (Researcher)
  2021 - 2023
• Indian Institute of Technology Mandi Research Scholar
  2015 - Present

Education

• University of Delhi M.A.(Hons)
  2011 - 2013
• University of Delhi B.A.(Hons)
  2008 - 2011

Projects & Funding

Projects & funding information is unavailable.

Publications (16)

• Oscillation of second-order non-canonical non-linear dynamic equations with a sub-linear neutral term
  Differential Equations and Dynamical Systems 2024 DOI: 10.1007/s12591-022-00592-0
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• A note on Sugeno exponential function with respect to distortion
  Applied Mathematics and Computation 2024 DOI: 10.1016/j.amc.2024.128586
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• Existence and uniqueness of solutions of differential equations with respect to non‐additive measures
  Mathematical Methods in the Applied Sciences 2023 DOI: 10.1002/mma.8637
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• Existence and uniqueness of solutions of differential equations with respect to non-additive measures
  2022 DOI: 10.22541/au.165165122.22320808/v1
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• Δ-Choquet integral on time scales with applications
  Chaos, Solitons & Fractals 2022 DOI: 10.1016/j.chaos.2022.111969
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• New oscillatory results for non-linear delay dynamic equations with super-linear neutral term
  Applied Mathematics and Computation 2022 DOI: 10.1016/j.amc.2021.126576
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• Delta-Choquet Integral on Time Scales with Applications
  2022 DOI: 10.2139/ssrn.4024034
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• Survey on Qualitative Theory of Dynamic Equations on Time Scale
  Memoirs on Differential Equations and Mathematical Physics 2021
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• A generalized delta derivative on time scale with applications
  Mathematical Methods in the Applied Sciences 2020 DOI: 10.1002/mma.6601
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• Periodic Solutions of the N-Preys and M-Predators Model with Variable Rates on Time Scales
  Indian Journal of Pure and Applied Mathematics 2020 DOI: 10.1007/s13226-020-0443-3
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