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Nonlinear F-contractions on b-metric spaces and differential equations in the frame of fractional derivatives with Mittag–Leffler kernel
Journal article   Peer reviewed

Nonlinear F-contractions on b-metric spaces and differential equations in the frame of fractional derivatives with Mittag–Leffler kernel

Badr Alqahtani, Andreea Fulga, Fahd Jarad and Erdal Karapınar
Chaos, solitons and fractals, Vol.128, pp.349-354
11/2019
DOI: https://doi.org/10.1016/j.chaos.2019.08.002

Abstract

b-metric space Fractional derivative Nonlinear F-contraction
In this manuscript, we aim to refine and characterize nonlinear F-contractions in a more general framework of b-metric spaces. We investigate the existence and uniqueness of such contractions in this setting. We discuss the solutions to differential equations in the setting of fractional derivatives involving Mittag–Leffler kernels (Atangana–Baleanu fractional derivative) by using nonlinear F-contractions that indicate the genuineness of the presented result.

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