Chapter 3 - Fractional Evolution Inclusions with Hille-Yosida Operators

Abstract

This chapter deals with fractional evolution inclusions involving a nondensely defined closed linear operator satisfying the Hille-Yosida condition and source term of multivalued type in Banach spaces. First, a definition of integral solutions for fractional differential inclusions is given. Then the topological structure of solution sets is investigated. It is shown that the solution set is nonempty, compact, and, moreover, an Rδ-set. An example is given to illustrate the feasibility of the abstract results. The problem of controllability of these inclusions and topological structure of solution sets are considered too.