Mild solutions and controllability of fractional evolution inclusions of Clarke's subdifferential type with nonlocal conditions in Hilbert spaces

Abstract

In this work, our aim is to ensure the existence of mild solutions and study the controllability of fractional evolution inclusions of Clarke's subdifferential type of order q∈(1,2) with nonlocal conditions in the setting of Hilbert spaces. Using fixed point techniques, fractional calculus, multivalued maps, cosine and sine function operators, we discuss the existence of mild solutions for the considered system. Moreover, under suitable conditions, we investigate the controllability of the proposed system. Finally, we present an illustrated example.