On an Initial Value Problem for Nonconvex-Valued Fractional Differential Inclusions in a Banach Space

Based on fixed point theory for condensing operators, an initial value problem for semilinear differential inclusions of fractional order $q\in(1,2)$ in Banach spaces is studied. It is assumed that the linear part of the inclusion generates a family of cosine operator functions, and the nonlinear part is a multivalued map with nonconvex values. Local and global existence theorems for integral solutions of the initial value problem are proved.