Numerical modeling of fractional-diffusion neurological disorder model: detection and infection-induced mortality chaos control

Volume 39, Issue 2, pp 131--159 https://dx.doi.org/10.22436/jmcs.039.02.01

Publication Date: March 22, 2025 Submission Date: July 09, 2024 Revision Date: September 04, 2024 Accteptance Date: January 14, 2025

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Authors

M. Farman - Faculty of Arts and Sciences, Department of Mathematics, Near East University, Northren Cyprus, Turkey. - Faculty of Art and Science, University of Kyrenia, Kyrenia, TRNC, Mersin 10, North Cyprus, Turkey. M. Ghannam - Faculty of Arts and Sciences, Department of Mathematics, Near East University, Northren Cyprus, Turkey. - Mathematical research center, Department of Mathematics, Near East University, Northren Cyprus, Turkey. K. S. Nisar - Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj, Saudi Arabia. - Saveetha School of Engineering, SIMATS, Chennai, India. E. Hincal - Faculty of Arts and Sciences, Department of Mathematics, Near East University, Northren Cyprus, Turkey. - Mathematical research center, Department of Mathematics, Near East University, Northren Cyprus, Turkey. B. Kaymakamzade - Faculty of Arts and Sciences, Department of Mathematics, Near East University, Northren Cyprus, Turkey. - Mathematical research center, Department of Mathematics, Near East University, Northren Cyprus, Turkey.

Abstract

This paper aims to investigate neurological disorder using a fractional-order Caputo operator for infection-induced mortality control and treatment, highlighting the importance of mathematical models in studying dynamical systems and understanding global diseases. Some essential properties are studied for the biological feasibility of the model, such as positivity, boundedness, and uniqueness of the system, with Arzela-Ascoli and Schauder's fixed point theory. The study presents an analytical analysis of a model using the fractional order Caputo operator, derived through an iterative formula. It also proves the Picard P-stable results and the reproductive number based on equilibrium points and sensitivity index. The model's stability is studied using the Lyapunov function, and chaos control and flip bifurcation results demonstrate the feasibility of solutions for various infection consequences. Numerical results are obtained using the Newton polynomial interpolation method, and simulations are conducted to verify the effectiveness of the proposed scheme and understand the dynamics of infection in brain cells at different fractional order values. The study reveals that fractional modelling provides crucial insights into the dynamic behavior of infectious brain disorders, aiding in a comprehensive understanding of their epidemiology and potential control methods.

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Keywords

• Neurological disorder
• Caputo operator
• Lyapunov function
• chaos control
• flip bifurcation
• Newton polynomial interpolation

MSC

•  26A33
•  34A08
•  37N25
•  92C30

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