Approximate Controllability of Fractional Impulsive Partial Neutral Stochastic Differential Inclusions with State-Dependent Delay and Fractional Sectorial Operators

Abstract

ABSTRACTIn this article, the approximate controllability of fractional impulsive partial neutral stochastic differential inclusions with state-dependent delay and fractional sectorial operators in Hilbert spaces is studied. By using the stochastic analysis, the fractional sectorial operators and a fixed point theorem for multi-valued maps combined with approximation techniques, we discuss a new set of sufficient conditions for the approximate controllability of the systems under the mixed Lipschitz and Carathéodory conditions. An example is provided to illustrate the obtained theory.