Study of impulsive problems under Mittag-Leffler power law

Mohammed S Abdo; Thabet Abdeljawad; Kamal Shah; Fahd Jarad

doi:10.1016/j.heliyon.2020.e05109

Study of impulsive problems under Mittag-Leffler power law

Heliyon. 2020 Oct 2;6(10):e05109. doi: 10.1016/j.heliyon.2020.e05109. eCollection 2020 Oct.

Authors

Mohammed S Abdo¹, Thabet Abdeljawad^{2

3

4}, Kamal Shah⁵, Fahd Jarad⁶

Affiliations

¹ Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen.
² Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
³ Department of Medical Research, China Medical University, Taichung 40402, Taiwan.
⁴ Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan.
⁵ Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan.
⁶ Department of Mathematics, Çankaya University, 06790 Etimesgut, Ankara, Turkey.

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: Atangana-Baleanu-Caputo operator; Existence theory; Fixed point theorem; Fractional impulsive problems; Mathematics.