Vol. 6 No. 2 (2022): Vol 6, Iss 2, Year 2022
Stochastic fractional differential equations with generalized Caputo's derivative and impulsive effects
Published December 31, 2022
- 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
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.
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