Existence Results of Nonlocal Fractional Integro-Neutral Differential Inclusions with Infinite Delay

Abstract

This article addresses a new class of delayed fractional multivalued problems complemented with nonlocal boundary conditions. In view of infinite delay theory, we convert the inclusion problem into a fixed-point multivalued problem, defined in an appropriate phase space. Then, sufficient criteria for the existence of solutions are established for the convex case of the given problem using the nonlinear Leray–Schauder alternative type, while Covitz and Nadler’s theorem is applied for nonconvex multivalued functions. Finally, the results are illustrated through examples.

Keywords

• fractional derivative
• inclusions
• delay
• fixed point
• nonlocal boundary condition