Some existence and uniqueness results for a class of proportional Liouville-Caputo fractional stochastic differential equations

Abstract

This paper is devoted to a systematic discussion of the existence and uniqueness of solution of a family of proportional Liouville-Caputo fractional stochastic differential equations by applying the Banach fixed point technique. We investigate the theory of the Ulam-Hyers-Rassias stability with respect to (ε,θ(ϑ)) of proportional Liouville-Caputo fractional stochastic differential equations by making use of the classical techniques of stochastic calculus and the Banach fixed point technique. Two examples are presented in order to illustrate our main results.