Mathematical analysis of neurological disorder under fractional order derivative

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.

Keywords

• fractional operator
• existence theory
• numerical method
• unique solution