Vol. 6 No. 2 (2022): Vol 6, Iss 2, Year 2022
Articles

Stochastic Fractional Differential Equations With Generalized Caputo’s Derivative and Impulsive Effects

PDF
  • Archana Chauhan,
  • Ganga Ram Gautam,
  • Jitendra Kumar,
  • Jaydev Dabas,
  • S.P.S. Chauhan
Archana Chauhan
Ex-Department of Applied Sciences, Galgotias College of Engineering and Technology, Greater Noida-201310, India.
Ganga Ram Gautam
DST-Centre for Interdisciplinary Mathematical Science,Institute of Science, Banaras Hindu University, Varanasi-221005,India.
Jitendra Kumar
Department of Applied Mathematics and Scientific Computing, IIT Roorkee, Saharanpur Campus, Saharanpur-247001, India.
Jaydev Dabas
Department of Applied Mathematics and Scientific Computing, IIT Roorkee, Saharanpur Campus, Saharanpur-247001, India.
S.P.S. Chauhan
School of Computer Science Engineering, Galgotias University, Greater Noida - 201306, India.
DOI: https://doi.org/10.26524/cm152
Published December 31, 2022
Keywords
  • Stochastic fractional differential equations, Impulsive condition, Generalized Caputo’s derivative, Existence and uniqueness of solutions, Continuity of solutions.
How to Cite
Archana Chauhan, Ganga Ram Gautam, Jitendra Kumar, Jaydev Dabas, & S.P.S. Chauhan. (2022). Stochastic Fractional Differential Equations With Generalized Caputo’s Derivative and Impulsive Effects. Journal of Computational Mathematica, 6(2), 093-115. https://doi.org/10.26524/cm152

Abstract

In this paper, impulsive stochastic fractional differential equations (ISFDEs) in Lp(p ≥ 2) space are introduced. We present a general framework for finding solution for ISFDEs. Then, by using the Burkholder - Davis - Gundy inequality and Holder’s inequality, we prove the existence and uniqueness of solution to ISFDE by fixed point theorem. We also investigate Lipschitz continuity of solutions with respect to initial values by using Gronwall inequality. Finally, we provide an application to illustrate the results we obtained.

PDF

Downloads

Download data is not yet available.