Topological Structure and Existence of Solutions Set for q-Fractional Differential Inclusion in Banach Space

Abstract

In this work, we concentrate on the existence of the solutions set of the following problem cDqασ(t)∈F(t,σ(t),cDqασ(t)),t∈I=[0,T]σ0=σ0∈E, as well as its topological structure in Banach space E. By transforming the problem posed into a fixed point problem, we provide the necessary conditions for the existence and compactness of solutions set. Finally, we present an example as an illustration of main results.