On the Existence and Stability of a Neutral Stochastic Fractional Differential System

The main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) of solutions of a nonlinear neutral stochastic fractional differential system. We prove the existence and uniqueness of solutions to the proposed system by using fixed point theorems and the Banach contraction principle. Also, by using fundamental schemes of fractional calculus, we study the (U-Hs) to the solutions of our suggested system. Besides, we study an example, best describing our main result.

Automated summary

The main purpose of this paper is to investigate the existence and Ulam-Hyers stability of solutions of a nonlinear neutral stochastic fractional differential system. The existence and uniqueness of solutions to the proposed system are proved by using fixed point theorems and the Banach contraction principle. Additionally, the stability of the solutions to the suggested system is studied using fundamental schemes of fractional calculus. An example is also provided to illustrate the main result.