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

# Stochastic fractional differential equations with generalized Caputo's derivative and impulsive effects

Archana Chauhan
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.
Chauhan S P S
School of Computer Science Engineering, Galgotias University, Greater Noida - 201306, India.
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
Chauhan, A., Gautam, G. R., Kumar, J., Dabas, J., & S P S, C. (2022). Stochastic fractional differential equations with generalized Caputo’s derivative and impulsive effects. Journal of Computational Mathematica, 6(2), 93-115. 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.