EXISTENCE RESULTS FOR RIEMANN-LIOUVILLE FRACTIONAL EVOLUTION INCLUSIONS.

In recent years, differential inclusions with fractional order have been extensively studied by many authors. However, up to now fractional evolution inclusions with Riemann- Liouville derivative have not been considered in the literature. In order to fill this gap, in this paper we establish sufficient conditions for the existence of solutions of fractional evolution inclusions involving the Riemann-Liouville fractional derivative. The cases of convex-valued and nonconvex-valued right-hand sides are considered and we present a version of Filippov's theorem for fractional semilinear differential inclusions with Riemann-Liouville derivative. [ABSTRACT FROM AUTHOR]