Existence of Solutions for Fractional Partial Neutral Stochastic Functional Integro-Differential Inclusions with State-Dependent Delay and Analytic Resolvent Operators

Abstract

We investigate the existence of mild solutions for a class of fractional partial neutral stochastic functional integro-differential inclusions with state-dependent delay and analytic α-resolvent operators in Hilbert spaces. Sufficient conditions for the existence are established by using the nonlinear alternative of Leray–Schauder type for multivalued maps due to O’Regan and the fractional power of operators. An example is provided to illustrate the obtained theory.