New Outcomes Regarding the Existence of Hilfer Fractional Stochastic Differential Systems via Almost Sectorial Operators

Abstract

In this paper, we focus on the existence of Hilfer fractional stochastic differential systems via almost sectorial operators. The main results are obtained by using the concepts and ideas from fractional calculus, multivalued maps, semigroup theory, sectorial operators, and the fixed-point technique. We start by confirming the existence of the mild solution by using Dhage’s fixed-point theorem. Finally, an example is provided to demonstrate the considered Hilferr fractional stochastic differential systems theory.