@article{Khan2023, 
author = {Nadeem Khan and Amjad Ali and Aman Ullah and Zareen A. Khan},
title = {Mathematical analysis of neurological disorder under fractional order derivative},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {18846-18865},
keywords = {numerical method, unique solution, existence theory, fractional operator},
url = {https://www.sciopen.com/article/10.3934/math.2023959},
doi = {10.3934/math.2023959},
abstract = {Multiple sclerosis (MS) is a common neurological disorder that affects the central nervous system (CNS) and can cause lesions that spread over space and time. Our study proposes a mathematical model that illustrates the progression of the disease and its likelihood of recurrence. We use Caputo fractional-order (FO) derivative operators to represent non-negative solutions and to establish a steady-state point and basic reproductive number. We also employ functional analysis to prove the existence of unique solutions and use the Ulam-Hyres (UH) notion to demonstrate the stability of the solution for the proposed model. Furthermore, we conduct numerical simulations using an Euler-type numerical technique to validate our theoretical results. Our findings are presented through graphs that depict various behaviors of the model for different parameter values.}
}