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Existence and stability for a nonlinear hybrid differential equation of fractional order via regular Mittag–Leffler kernel
Journal article   Peer reviewed

Existence and stability for a nonlinear hybrid differential equation of fractional order via regular Mittag–Leffler kernel

Ibrahim Slimane, Zoubir Dahmani, Juan J. Nieto and Thabet Abdeljawad
Mathematical methods in the applied sciences, Vol.46(7), pp.8043-8053
15/05/2023
DOI: https://doi.org/10.1002/mma.7349

Abstract

Atangana–Baleanu derivative hybrid differential equations Ulam–Hyers stability
This paper deals with a nonlinear hybrid differential equation written using a fractional derivative with a Mittag–Leffler kernel. Firstly, we establish the existence of solutions to the studied problem by using the Banach contraction theorem. Then, by means of the Dhage fixed‐point principle, we discuss the existence of mild solutions. Finally, we study the Ulam–Hyers stability of the introduced fractional hybrid problem.

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