Abstract
In this work, we concentrate on the existence of the solutions set of the following problem D-c(q)alpha sigma(t) is an element of F(t, sigma(t),D-C(q)alpha sigma(t)),t is an element of I = [0, T] sigma(0) = sigma(0) is an element of 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.