On fractional state-dependent delay integro-differential systems under the Mittag-Leffler kernel in Banach space

Abstract

The existence of Atangana-Baleanu fractional-order semilinear integro-differential systems and semilinear neutral integro-differential systems with state-dependent delay in Banach spaces is investigated in this paper. We establish the existence findings by using Monch's fixed point theorem and the concept of measures of non-compactness. A functioning example is provided at the end in order to illustrate the findings reached from the theoretical study.

Keywords

• ab fractional-order derivative
• mild solution
• state-dependent delay
• fixed point theorem (fpt)