Theoretical and Computational Analysis of Coupled System of Multiple Sclerosis Using Non-singular Type Derivative

Authors

  • Ghazala Nazir Department of Mathematics, Mohi ud Din University Nerian Sharif AJ\&K Likhna
  • Rahmat Ali Khan
  • Faheem Yaqoob Department of Computer Sciences, Faculty of Basic Science, University of Poonch ,Rawalakot Azad Kashmir, Pakistan
  • Sadique Ahmad IAS Data Science and BlockChain Laboratory, College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
  • Mohammed A.Elaffendi IAS Data Science and BlockChain Laboratory, College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
  • Abdelhamied Ashraf Ateya IAS Data Science and BlockChain Laboratory, College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v19i2.6482

Keywords:

Neural disease model; non-singular derivative; Existence theory; Numerical results.

Abstract

In this study, we develop and analyze a mathematical model for multiple sclerosis (MS), a progressive neurological disorder of the central nervous system. One of its main properties is the dissemination of lesions in time and space. The model is constructed within the framework
of non-singular fractional derivatives of non-integer order. Using nonlinear functional analysis, we establish key qualitative properties of the system, including existence and stability of solutions. The Banach and Krasnoselskii fixed point theorems are applied to demonstrate solution existence, while stability is investigated through the Hyers-Ulam approach. For the numerical approximation of the
model’s compartments, an Adams-Bashforth method is employed, and simulations are presented to illustrate the dynamic behavior of the system under varying fractional orders. The results indicate that modeling with non-singular fractional derivatives provides a powerful framework for exploring neurodegenerative disorders and holds potential for enhancing strategies to predict and manage the progression of MS.

Author Biographies

  • Faheem Yaqoob, Department of Computer Sciences, Faculty of Basic Science, University of Poonch ,Rawalakot Azad Kashmir, Pakistan

    He is teacher in Department of Computer Sciences, Faculty of  Basic Science, University of Poonch ,Rawalakot Azad Kashmir, Pakistan

  • Sadique Ahmad, IAS Data Science and BlockChain Laboratory, College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

    Researcher in IAS Data Science and BlockChain Laboratory, College of Computer and Information Sciences, Prince Sultan University,
    Riyadh 11586, Saudi Arabia

  • Mohammed A.Elaffendi, IAS Data Science and BlockChain Laboratory, College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

    Professor in IAS Data Science and BlockChain Laboratory, College of Computer and Information Sciences, Prince Sultan University,
    Riyadh 11586, Saudi Arabia

  • Abdelhamied Ashraf Ateya, IAS Data Science and BlockChain Laboratory, College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

    Researcher in IAS Data Science and BlockChain Laboratory, College of Computer and Information Sciences, Prince Sultan University,
    Riyadh 11586, Saudi Arabia

References

Published

2026-07-28

Issue

Vol. 19 No. 2: (April 2026)

Section

Mathematical Biosciences

License

Copyright (c) 2026 Ghazala Nazir, Rahmat Ali Khan, Faheem Yaqoob, Sadique Ahmad, Mohammed A.Elaffendi, Abdelhamied Ashraf Ateya

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How to Cite

Theoretical and Computational Analysis of Coupled System of Multiple Sclerosis Using Non-singular Type Derivative. (2026). European Journal of Pure and Applied Mathematics, 19(2), 6482. https://doi.org/10.29020/nybg.ejpam.v19i2.6482