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.

Keywords

• Λ-continuity
• <i>σ</i>-self-closed relations
• binary relations