A note on approximate controllability for nonlocal fractional evolution stochastic integrodifferential inclusions of order [formula omitted] with delay

Abstract

In this paper, we formulate a new set of sufficient conditions for the approximate controllability of fractional evolution stochastic integrodifferential delay inclusions of order r∈(1,2) with nonlocal conditions in Hilbert space. Martelli’s fixed point theorem, multivalued functions, cosine and sine families, fractional calculus and operator semigroups are used to establish the results under the assumption that the corresponding linear system is approximately controllable. Finally, an example is provided to illustrate the applicability of the obtained theoretical results.