Approximate Solution of coupled differential equations system for Corona disease based on the Second Kind Chebyshev Polynomial

Atabakzadeh, Mohammad Hadi; Dehghan, Jamileh; Alizadeh, Mahmoud; Shokrollahi Yancheshmeh, Sara

doi:10.22055/jamm.2026.49602.2382

Approximate Solution of coupled differential equations system for Corona disease based on the Second Kind Chebyshev Polynomial

Document Type : Original Paper

Authors

Mohammad Hadi Atabakzadeh ¹

Jamileh Dehghan ²

Mahmoud Alizadeh ²

Sara Shokrollahi Yancheshmeh ²

¹ Department of Mathematics, Bu . C, Islamic Azad University, Bushehr, Iran

² Department of Mathematics, Ahv .C, Islamic Azad University, Ahvaz, Iran

10.22055/jamm.2026.49602.2382

Abstract

In this paper, a system of coupled fractional differential equations that models the spread of
COVID-19 infection between two population groups, ”with symptoms of infection” (φ(t)) and ”without
symptoms of infection” (ω(t)), is investigated. The proposed method is based on the Second Kind
Chebyshev Polynomial with the Atangana-Baleanu fractional derivative and integral. The main innovation
of this paper is to superiority of the accuracy and efficiency of this method compared to the conventional
first-order Chebyshev method and the fourth-order Runge-Kutta method (RK4). For objective evaluation,
the Mean Squared Error (MSE) and Mean Absolute Error (MAE) criteria were calculated. Numerical results
for different values of the fractional order (ν) show that the proposed method has higher accuracy
and efficiency with an MSE of about 10(−4) and an exponential convergence rate. These findings confirm
the high potential of the present method for more accurate modeling of epidemiological phenomena

Keywords

coupled differential equations system

Corona disease

Second Kind Chebyshev Polynomial

Atangana-Baleanu fractional derivative and integral

Subjects