Study on stochastic fractional differential equations with random impulse

Abstract

This manuscript is devoted to prove existence and stability results of random impulsive stochastic fractional differential equations(ISFDE's). Initially, a system is developed and the existence results of mild solutions are obtained using Banach Contraction Principle. By the use of Stochastic analysis techniques and sufficient conditions the results are formulated. Then, using continuous dependency of solutions on initial conditions, we establish the stability results. Finally, to demonstrate our results, an example is provided.