Some Existence and Uniqueness Results for a Class of Fractional Stochastic Differential Equations

Abstract

Many techniques have been recently used by various researchers to solve some types of symmetrical fractional differential equations. In this article, we show the existence and uniqueness to the solution of ς-Caputo stochastic fractional differential equations (CSFDE) using the Banach fixed point technique (BFPT). We analyze the Hyers–Ulam stability of CSFDE using the stochastic calculus techniques. We illustrate our results with three examples.

Keywords

• fractional calculus
• fixed-point theory