Study of impulsive problems under Mittag-Leffler power law

Abstract

This article is fundamentally concerned with deriving the solution formula, existence, and uniqueness of solutions of two types of Cauchy problems for impulsive fractional differential equations involving Atangana-Baleanu-Caputo (ABC) fractional derivative which possesses nonsingular Mittag-Leffler kernel. Our investigation is based on nonlinear functional analysis and some fixed point techniques. Besides, some examples are given delineated to illustrate the effectiveness of our outcome.

Keywords

• Mathematics
• Fractional impulsive problems
• Atangana-Baleanu-Caputo operator
• Existence theory
• Fixed point theorem