Solving multi-order fractional differential equations using covariant contraction principle

Volume 39, Issue 1, pp 71--89 https://dx.doi.org/10.22436/jmcs.039.01.05

Publication Date: March 12, 2025 Submission Date: October 29, 2024 Revision Date: January 23, 2025 Accteptance Date: February 01, 2025

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Authors

N. Hussain - Department of Mathematics, King Abdulaziz University, Jeddah, 80203, 21589, Saudi Arabia. N. Alharbi - Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia. G. Basendwah - Department of Mathematics, King Abdulaziz University, Jeddah, 80203, 21589, Saudi Arabia.

Abstract

This article introduces the concept of a generalized fuzzy bipolar metric space which extends the framework of fuzzy bipolar metric spaces. Within this novel setting, we establish the Ćirić quasi-contraction theorem tailored to generalized fuzzy bipolar metric spaces. To achieve these results, we introduce the notions of covariant and contravariant contractions, which represent significant advances in this field. To illustrate the applicability of the theoretical findings, detailed examples are provided. Moreover, the study delves into the well-posedness of the fuzzy fixed point problem, demonstrating the existence and uniqueness of solutions for multi-order fractional differential equations.

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Keywords

• Generalized fuzzy bipolar metric space
• fuzzy fixed point results
• well-posedness of fixed point problem
• multi-order fractional differential equations
• integral boundary conditions

MSC

•  54H25
•  34A08
•  34A12

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