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

Author

Listed:
  • KAMAL SHAH

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia†Department of Mathematics, University of Malakand, Dir(L), 18000, Khyber Pakhtunkhwa, Pakistan)

  • BAHAAELDIN ABDALLA

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • THABET ABDELJAWAD

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia‡Department of Medical Research, China Medical University, Taichung 40402, Taiwan§Department of Mathematics Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea¶Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho, Health Sciences University, Ga-Rankuwa, South Africa)

  • MANAR A. ALQUDAH

    (College of Science, Princess Nourah bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia)

Abstract

A mathematical model of progressive disease of the nervous system also called multiple sclerosis (MS) is studied in this paper. 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 (HU) 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.

Suggested Citation

  • Kamal Shah & Bahaaeldin Abdalla & Thabet Abdeljawad & Manar A. Alqudah, 2024. "A Fractal-Fractional Order Model To Study Multiple Sclerosis: A Chronic Disease," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(02), pages 1-13.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:02:n:s0218348x24400103
    DOI: 10.1142/S0218348X24400103
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