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

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

doi:10.1142/S0218348X24400103

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

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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.

Original language	English
Article number	2440010
Journal	Fractals
Volume	32
Issue number	2
DOIs	https://doi.org/10.1142/S0218348X24400103
Publication status	Published - 2024
Externally published	Yes

Keywords

Fixed Point Theorem
Fractal-Fractional Order Derivative
HU Stability
Numerical Results
Progressive Disease

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10.1142/S0218348X24400103

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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.",

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AU - Shah, Kamal

AU - Abdalla, Bahaaeldin

AU - Abdeljawad, Thabet

AU - Alqudah, Manar A.

PY - 2024

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AB - 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.

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

Abstract

Keywords

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