ANALYSIS OF IMPULSIVE FRACTIONAL DELAY DIFFERENTIAL EQUATIONS WITH MITTAG-LEFFLER KERNEL AND ITS APPLICATIONS TO HUTCHINSON’S MODEL

Abstract

In this paper, we use the Schuader fixed point and the Banach contraction principle to study sufficient conditions for existence, uniqueness, and Lipschitz stability of solutions for fractional delay differential equations with Mittag-Leffler Kernel (without impulses) and impulsive fractional differential equations (with delay). As a result, with practical applications, the theoretical understanding of fractional differential equations containing memory effects, impulse perturbations, and delay factors is expanded. The developed concept is finally illustrated with examples and applied to impulsive fractional delay biological systems involving a single species population growth model known as, the Hutchinson’s equations using the fractional order derivative with Mittag-Leffler kernel.