OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 14 3 2024 07 24 Collocation Method for Solving Systems of Fractional Differential Equations, A Case Study of HIV Infection by Using Muntz Wavelets Basis 187 199 10.71932/ijm.2024.1195092 EN Maryam Bahmanpour Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran. Journal Article 2024 07 24 This work was written with the aim of solving the fractional differential equation system using the Muntz wavelets. Muntz wavelets are modified using polynomials, respectively. The error of the proposed method is evaluated. This method applies to the fractional version of the HIV infection model. Numerical results confirm the accuracy of the proposed method. In the present work, in the  first stage the Muntz wavelets are introduced. These wawelets are definitely faster and more accurate than the Muntz Legendre polynomials.In the second stage the M\"{u}ntz Legendre polynomials in the interval [0,1] are introduced.In the continuation of the stages the definitions and properties of wavelets will be discussed.The Muntz wavelets are then presented in the range  [0, T]. Subsequently, with the help of Jacobi polynomials, a more stable formula for Muntz wavelets is obtained. Finally the fractional differential equations are solved and the error analysis is reviewed. Also, to investigate of the accuracy of the presented method, mathematical and practical examples are presented.