Fractional semilinear differential inclusions

In this paper, we first present a version of Filippov’s Theorem for fractional semilinear differential inclusions of the form, {(cDαy−Ay)(t)∈F(t,y(t)), a.e. t∈[0,b],y(0)=y0∈X, where cDαcDα is the Caputo fractional derivative and FF is a set-valued map. After several existence results, the compactness of solutions sets is also investigated. Some results from topological fixed point theory together with notions of measure of noncompactness are used.