University of Guilan Journal of Mathematical Modeling 2345-394X 11 3 2023 10 01 An efficient approach for solving the fractional model of the human T-cell lymphotropic virus I by the spectral method 463 477 6647 10.22124/jmm.2023.23219.2150 EN Mahboubeh Molavi-Arabshahi Mathematical modeling laboratory, School of Mathematics, Iran University of Science and Technology, Narmak 16844, Tehran, Iran Rashidinia Jalil Mathematical modeling laboratory, School of Mathematics, Iran University of Science and Technology, Narmak 16844, Tehran, Iran Mahnaz Yousefi Mathematical modeling laboratory, School of Mathematics, Iran University of Science and Technology, Narmak 16844, Tehran, Iran Journal Article 2023 03 07 This paper aims to present a new and efficient numerical method to approximate the solution of the fractional model of human T-cell lymphotropic virus I (HTLV-I) infection $CD4^+T$-cells. The approximate solution of the model is obtained using the shifted Chebyshev collocation spectral method. This model relates to the class of nonlinear ordinary differential equations. The proposed algorithm reduces the Caputo sense fractional model to a system of nonlinear algebraic equations that can be solved numerically. The convergence of the proposed method is investigated. The graphical result is compared with existing numerical methods reported in the literature to indicate the efficiency and reliability of the presented method. https://jmm.guilan.ac.ir/article_6647_b3c7d526a8cf2c86ee43b170b57cb356.pdf