Variable-Order Fractional Differential Equations: Existence, Stability, and Application to 3D Noise Evolution

Authors

  • Tharmalingam Gunasekar Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Chennai - 600062, Tamil Nadu, India
  • Jaya Priya Dhanasekar Department of Mathematics, Vel Tech Rangarajan Dr.Sagunthala R&D Institute of Science and Technology, Chennai - 600062, Tamil Nadu, India
  • Nidal Anakira Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, Oman
  • Osama Ogilat Department of Basic Sciences, Faculty of Arts and Science, Al-Ahliyya Amman University, Amman, Jordan
  • Amani Sheimat Department of Basic Sciences, Faculty of Arts and Science, Al-Ahliyya Amman University, Amman 19111, Jordan

DOI:

https://doi.org/10.19139/soic-2310-5070-4095

Keywords:

Fractional boundary value problems, Variable-orer fractional calculus, Krasnoselskii fixed point theorem;, Existence and uniqueness

Abstract

This paper studies a boundary value (BV) problem characterized by variable order(VO) Caputo fractionalderivatives to study the existence, uniqueness, and stability of solutions under well-defined boundary conditions. Fixedpoint theory is used, where the Banach contraction principle ensures the uniqueness of solutions, while the Krasnoselskiitheorem confirms their existence. Furthermore, the notion of Ulam-Hyers stability is used to investigate the response of thesolutions to small perturbations. Numerical examples are presented to illustrate the theoretical results and to validate theapproach under practical conditions. Additionally, an application concerning the evolution of features in three - dimensionalnoise fields is included. The highlights its engineering relevance, particularly in image processing and signal analysis, wheremodeling noise behavior and memory effects is important for tasks such as denoising and feature extraction

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Published

2026-06-09

How to Cite

Tharmalingam Gunasekar, Jaya Priya Dhanasekar, Anakira, N., Osama Ogilat, & Sheimat, A. (2026). Variable-Order Fractional Differential Equations: Existence, Stability, and Application to 3D Noise Evolution. Statistics, Optimization & Information Computing, 16(1), 641–659. https://doi.org/10.19139/soic-2310-5070-4095

Issue

Vol. 16 No. 1 (2026)

Section

Research Articles

License

Copyright (c) 2026 Nidal Anakira, Jaya Priya Dhanasekar, Tharmalingam Gunasekar, Osama Ogilat, mani Sheimat

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