Solving Fractional Differential Equations via New Relation-Theoretic Fuzzy Fixed Point Theorems

Waleed M. Alfaqih (), Salvatore Sessa (), Hayel N. Saleh and Mohammad Imdad
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Waleed M. Alfaqih: Department of Mathematics, Hajjah University, Hajjah 00967, Yemen
Salvatore Sessa: Dipartimento di Architettura, Università Degli Studi di Napoli Federico II, Via Toledo 402, 80134 Napoli, Italy
Hayel N. Saleh: Department of Mathematics, Taiz University, Taiz 00967, Yemen
Mohammad Imdad: Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India

Mathematics, 2025, vol. 13, issue 16, 1-13

Abstract: In this paper, we present the notion of fuzzy R − F − contractive mappings and provide some fuzzy fixed point results in the setting of fuzzy metric spaces, which are endowed with binary relations. Furthermore, we apply our newly established fuzzy fixed point results to solve certain boundary value problems for nonlinear fractional differential equations involving the Caputo fractional derivatives. Also, we provide some examples to show the utility of our new results.

Keywords: Caputo fractional differential equation; fixed point; binary relation; R − F −contractive mappings; fuzzy metric space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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