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

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  • Waleed M. Alfaqih

    (Department of Mathematics, Hajjah University, Hajjah 00967, Yemen
    Faculty of Medical Technology, 21 September University for Medical and Applied Sciences, Sana’a 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)

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.

Suggested Citation

  • Waleed M. Alfaqih & Salvatore Sessa & Hayel N. Saleh & Mohammad Imdad, 2025. "Solving Fractional Differential Equations via New Relation-Theoretic Fuzzy Fixed Point Theorems," Mathematics, MDPI, vol. 13(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:16:p:2582-:d:1722998
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