Solvability of a State–Dependence Functional Integro-Differential Inclusion with Delay Nonlocal Condition

Abstract

There is great focus on phenomena that depend on their past history or their past state. The mathematical models of these phenomena can be described by differential equations of a self-referred type. This paper is devoted to studying the solvability of a state-dependent integro-differential inclusion. The existence and uniqueness of solutions to a state-dependent functional integro-differential inclusion with delay nonlocal condition is studied. We, moreover, conclude the existence of solutions to the problem with the integral condition and the infinite-point boundary one. Some properties of the solutions are given. Finally, two examples illustrating the main result are presented.

q -fractional functional integro-differential equation with q -integral condition

“…Importance of fractional differential equations appears in many of the physical and engineering phenomena [13]. Problems with non-local conditions and related topics were studied, for example [6,7,9]. The attention of researchers subject of q-differential equations appeared in recent years [17].…”