# A Legendre Tau method for numerical solution of multi-order fractional mathematical model for COVID-19 disease

Document Type : Research Paper

Authors

1 Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.

2 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.

Abstract

In this paper, we describe a spectral Tau approach for approximating the solutions of a system of multi-order fractional differential equations which resulted from coronavirus disease mathematical modeling (COVID-19). The non-singular fractional derivative with a Mittag-Leffler kernel serves as the foundation for the fractional derivatives. Also, the operational matrix of fractional differentiation on the domain [0, a] is presented. Then, the convergence analysis of the proposed approximate approach is established and the error bounds are determined in a weighted L2 norm. Finally, by applying the Tau method, some of the important parameters in the model’s impact on the dynamics of the disease are graphically displayed for various values of the non-integer order of the ABC-derivative.

Keywords

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### History

• Receive Date: 30 August 2022
• Revise Date: 09 April 2023
• Accept Date: 10 April 2023