No 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.Keywords Stochastic integro-differential inclusions · State-dependent delay · Multi-valued map · Fractional neutral integro-differential inclusions · α-resolvent operator Mathematics Subject Classification (2010) 34A37 · 60H10 · 34K50 · 34G25 · 26A33