An Existence and Uniqueness of Solutions for a Stochastic Differential Equations with \psi-Caputo Fractional Derivative

Abstract

The present work investigates the existence and uniqueness of solutions for a fractional stochastic differential equations with $\psi$-Caputo fractional derivatives. We establish important theoretical conclusion and examine the energy growth bounds and asymptotic behavior of the stochastic solution using the Banach's fixed point theorem. Additionally, we consider our analysis into single-valued function derived from multivalued mappings. We provide examples to validate in our methodology.