Stochastic fractional differential equations with generalized Caputo's derivative and impulsive effects
- Stochastic fractional differential equations, Impulsive condition, Generalized Caputo's derivative, Existence and uniqueness of solutions, Continuity of solutions
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.