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 mild solutions of the initial value problem are proved.