ON THE CONTROLLABILITY PROBLEM FOR A SEMILINEAR FUNCTIONAL DIFFERENTIAL INCLUSION OF FRACTIONAL ORDER WITH INFINITE DELAY
In this paper we prove the existence of solutions and the compactness of the set of all solutions of the controllability problem for semilinear functional differential inclusion of fractional order with infinite delay and impulse characteristics in a Banach space. The paper consists of an introduction and four sections. In the introduction the urgency of this problem is justified. In the second section we describe the setting of the problem. The third section consists of four sub-sections dedicated to the preliminaries. In the fourth section we formulate and prove our main result (Theorem 4.1). In the last section as application we consider the controllability problem for a fractional diffusion process.