Relation-theoretic common fixed points for almost FR˜ℑ -contraction type maps in B2-metric spaces and application to nonlinear fractional differential equation

Abstract

This paper introduces a novel class of contraction mappings called ”almost FRℑ˜ -contraction type maps” in the framework of B2-metric spaces. These contractions are utilized to establish results regarding coincidence points and common fixed points furnished with a binary relation. Furthermore, the paper aims to broaden the scope of these findings by offering illustrative examples. The paper concludes with an application of these concepts to prove the existence of solutions of a nonlinear fractional differential equation. Our results broaden the scope of those reported in [16] and expand on comparable findings previously documented in the literature.