Topological structure of solution sets for fractional evolution inclusions of Sobolev type

Abstract

Abstract The paper is devoted to establishing the solvability and topological property of solution sets for the fractional evolution inclusions of Sobolev type. We obtain the existence of mild solutions under the weaker conditions that the semigroup generated by −AE−1 $-AE^{-1}$ is noncompact as well as F is weakly upper semicontinuous with respect to the second variable. On the same conditions, the topological structure of the set of all mild solutions is characterized. More specifically, we prove that the set of all mild solutions is compact and the solution operator is u.s.c. Finally, an example is given to illustrate our abstract results.

Keywords

• Fractional evolution inclusion
• Sobolev type
• Weakly upper semi-continuous
• Measures of noncompactness