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

Abstract

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. © 2019 Elsevier Ltd