Application on Atangana-Baleanu fractional derivative via (τ, a)-weak contractive mappings

Abstract

This paper introduces the innovative concept of (τ, a)-weak contractive mappings. We establish several fixed point results without relying on conditions essential in prior works. Examples are presented to showcase our key findings, particularly in scenarios where earlier research outcomes are not applicable. Furthermore, we provide an application of our obtained results to fractional differential equations involving non-singular and non-local kernels.