Fractional-Order Iterative BVPs: Uniqueness and Hyers-Ulam Stability

Authors

Muralee Bala Krushna Boddu Department of Mathematics, MVGR College of Engineering, Vizianagaram, Andhra Pradesh, 535005, India
Sumati Kumari Panda Department of Mathematics, GMR Institute of Technology, GMR Nagar, Rajam, Andhra Pradesh, 532127, India https://orcid.org/0000-0002-0220-8222
Hind Alamri Department of Mathematics, Faculty of Science, Taif University, Taif, 21974, Saudi Arabia
Nawab Hussain Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia https://orcid.org/0000-0001-6585-2202

DOI:

https://doi.org/10.37256/cm.7220268056

Keywords:

Caputo differential operator, iterative, boundary value problem, Kernel, two metrics, Rus's contraction mapping theorem, Hyers-Ulam stability

Abstract

This article investigates the existence and uniqueness of solutions to a fractional-order iterative boundary value problem characterized by Caputo derivatives. The analysis is conducted within the framework of Banach spaces, employing both the classical contraction principle and Schauder's fixed point approach to confirm the problem's solvability. Novel criteria ensuring the uniqueness of solutions are derived using Rus's contraction mapping theorem. The work also presents a detailed proof of the Hyers-Ulam stability for the proposed problem.

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Published

2026-03-06

How to Cite

Boddu MBK, Panda SK, Alamri H, Hussain N. Fractional-Order Iterative BVPs: Uniqueness and Hyers-Ulam Stability. Contemp. Math. [Internet]. 2026 Mar. 6 [cited 2026 Apr. 1];7(2):1874-92. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/8056

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Issue

Contemporary Mathematics, Volume 7 Issue 2 (2026)

Section

Research Article

License

This work is licensed under a Creative Commons Attribution 4.0 International License.