Non-instantaneous impulsive fractional-order delay differential systems with Mittag-Leffler kernel

Abstract

The existence of fractional-order functional differential equations with non-instantaneous impulses within the Mittag-Leffler kernel is examined in this manuscript. Non-instantaneous impulses are involved in such equations and the solution semigroup is not compact in Banach spaces. We suppose that the nonlinear term fulfills a non-compactness measure criterion and a local growth constraint. We further assume that non-instantaneous impulsive functions satisfy specific Lipschitz criteria. Finally, an example is given to justify the theoretical results.

Keywords

• atangana-baleanu fractional derivative
• non-instantaneous impulses
• mittag-leffler kernel
• fixed point theorem