A Fractal-Fractional Order Model to Study Multiple Sclerosis: A Chronic Disease

Kamal Shah, Bahaaeldin Abdalla, Thabet Abdeljawad, Manar A. Alqudah

Research output: Contribution to journalArticlepeer-review


A mathematical model of progressive disease of the nervous system also called multiple sclerosis (MS) is studied in this manuscript. The proposed model is investigated under the concept of the fractal-fractional order derivative (FFOD) in the Caputo sense. In addition, the tools of nonlinear functional analysis are applied to prove some qualitative results including the existence theory, stability, and numerical analysis. For the recommended results of the existence theory, Banach and Krassnoselski's fixed point theorems are used. Additionally, Hyers-Ulam (H-U) concept is used to derive some results for stability analysis. Additionally, for numerical illustration of approximate solutions of various compartments of the considered model, the modified Euler method is utilized. The aforementioned results are displayed graphically for various values of fractal-fractional orders.

Original languageEnglish
Publication statusAccepted/In press - 2023
Externally publishedYes


  • Fixed point theorem
  • Fractal-fractional order derivative
  • H-U stability
  • Numerical results
  • Progressive disease


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