Generalized fixed-point theorem for strict almost ϕ-contractions with binary relations in b-metric spaces and its application to fractional differential equations

Jiaojiao Wu; Fei  He; Shu-fang  Li

doi:10.59400/adecp2510

Jiaojiao Wu School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; School of Statistics and Mathematics, Inner Mongolia University of Financial and Economic, Hohhot 010070, China
Fei He School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Shu-fang Li School of Statistics and Mathematics, Inner Mongolia University of Financial and Economic, Hohhot 010070, China

Article ID: 2510

Keywords: fixed point; strict almost ϕ-contractions; binary relations; b-metric spaces; fractional differential equations

Abstract

The present study is centered around establishing a generalized fixed-point theorem for strict almost ϕ-contractions in b-metric spaces in the context of binary relations. Through the introduction of an innovative lemma, we offer distinct proof methodologies that diverge from the conventional ones in metric spaces. The achieved outcomes not only fortify but also broaden the domain of prior fixed-point theorems in the pertinent literature. Moreover, as a practical exemplification, the existence and uniqueness of solutions to fractional differential equations are illustrated convincingly, thereby connecting the theoretical and applied dimensions of the research.

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