Unique Solution Analysis for Generalized Caputo-Type Fractional BVP via Banach Contraction

Authors

  • Zouaoui Bekri Laboratory of fundamental and applied mathematics, University of Oran 1, Ahmed Ben Bella, Essenia, 31000 Oran, Algeria
  • Sarah Aljohani Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia
  • Mohammad Esmael Samei Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran
  • Ali Akg¨ul Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey
  • Abdelkader Belhenniche SYSTEC, Faculty of Engineering, Porto University, Institute for Systems and Robotics Rua Dr. Roberto Frias s/n, 4200-465 Porto, Portugal
  • Ahmad Aloqaily Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia
  • Nabil Mlaiki Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5979

Keywords:

Banach contraction theorem, Generalized Caputo fractional derivative, Boundary value problem, Existence and uniqueness

Abstract

In this manuscript, we investigate the existence of a unique solution to a boundary value problem (BVP) involving generalized fractional derivatives of the Caputo type. Our approach is grounded in the Banach contraction mapping theorem, which provides a rigorous framework for proving the existence of a fixed point and, consequently, a solution to the BVP. We extend this methodology to explore analogous problems, offering further insights and interpretations of the results derived from the main theorem. This work not only contributes to the theoretical understanding of fractional differential equations but also demonstrates how these techniques can be applied to a broader class of problems in mathematical physics and engineering. Through detailed analysis and extrapolation, we aim to establish a deeper connection between fractional calculus and fixed-point theory, providing a foundation for future research in this area.

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Published

2025-05-02

Issue

Vol. 18 No. 2: (April 2025)

Section

Differential Equations

License

Copyright (c) 2025 Zouaoui Bekri, Sarah Aljohani, Mohammad Esmael Samei, Ali Akg¨ul, Abdelkader Belhenniche, Ahmad Aloqaily, Nabil Mlaiki

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How to Cite

Unique Solution Analysis for Generalized Caputo-Type Fractional BVP via Banach Contraction. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5979. https://doi.org/10.29020/nybg.ejpam.v18i2.5979