Geraghty Type Contractions in Relational Metric Space with Applications to Fractional Differential Equations

Abstract

The present manuscript is devoted to investigating some existence and uniqueness results on fixed points by employing generalized contractions in the context of metric space endued with a weak class of transitive relation. Our results improve, modify, enrich and unify several existing fixed point theorems, The results proved in this study are utilized to find a unique solution of certain fractional boundary value problems.

Matkowski-Type Functional Contractions under Locally Transitive Binary Relations and Applications to Singular Fractional Differential Equations

“…In the recent past, fractional differential equations (FDEs for short) were discussed with regard to the impassable development and applicability of the area of fractional calculus. In recent years, some typical boundary value problems (BVPs for short) of FDEs have been solved using the fixed-point theorems proven in ordered metric space by Liang and Zhang [24] and Cabrera et al [25], relational metric space by Saleh et al [26] and Alamer et al [27], and orthogonal metric space by Abdou [28].…”