Existence and Stability of solution to a fractional mathematical model of the brain metabolite variations in the circadian rhythm containing Caputo derivative

Volume 39, Issue 3, pp 348--360 https://dx.doi.org/10.22436/jmcs.039.03.04

Publication Date: April 15, 2025 Submission Date: July 23, 2024 Revision Date: January 14, 2025 Accteptance Date: February 28, 2025

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Authors

E. A. A. Ziada - Basic Science Department, Nile Higher Institute for Engineering and Technology, Mansoura, Egypt. S. El-Morsy - Basic Science Department, Nile Higher Institute for Engineering and Technology, Mansoura, Egypt. - Department of Mathematics, College of Science and Arts, Qassim University, Al- Badaya 51951, Saudi Arabia.

Abstract

This study intends to investigate whether a solution to the model of brain metabolite variations in the circadian rhythm exists. The model is a fractional-order important model with regard to applications. The existence of a unique solution to the fractional brain model (FBM) with Caputo derivative is demonstrated, and the general form of the model is provided. A stability analysis is performed on the solution. In four different cases, the numerical solution to FBM is given using the proposed numerical method.

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Keywords

• Brain metabolites
• fractional mathematical model
• circadian rhythm
• existence and uniqueness
• fractional derivatives
• Caputo derivative
• proposed numerical method

MSC

•  34A12
•  34A34
•  45G05
•  92C50

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