Exactness of the solution to the stochastic fractional impulsive differential equations

This paper investigates the averaging principle for the solutions to stochastic fractional impulsive differential equations (SFIDEs) with nonlocal conditions. The main focus lies in deriving sufficient conditions for the convergence of the averaged SFIDEs. According to certain proposals, solutions to SFIDEs can be approximated by averaged stochastic systems using the mean square. Furthermore, two illustrative examples are provided to demonstrate the effectiveness of the proposed method in approximating the solutions to our model. The numerical simulations highlight the applicability and accuracy of the proposed approach in practical scenarios. This work contributes to the understanding and analysis of SFIDEs with complex conditions, paving the way for further research in the field of finance and industry.

کلیدواژه ها:

Fractional derivative ، Impulse ، Stochastic differential equation ، Brownian Motion ، Averaging method