A FRACTAL-FRACTIONAL ORDER MODEL TO STUDY MULTIPLE SCLEROSIS: A CHRONIC DISEASE

Kamal Shah, Bahaaeldin Abdalla (), Thabet Abdeljawad and Manar A. Alqudah ()
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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

FRACTALS (fractals), 2024, vol. 32, issue 02, 1-13

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.

Keywords: Progressive Disease; Fractal-Fractional Order Derivative; Fixed Point Theorem; HU Stability; Numerical Results (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400103

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