- - - Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
- - - Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

This paper deals with the application of fourth kind Chebyshev wavelets (FKCW) in solving numerically a model of HIV infection of CD۴+T cells involving Caputo fractional derivative. The present problem is a system of nonlinear fractional differential equations. The goal is to approximate the solution in the form of FKCW truncated series. To do this, an operational matrix of fractional integration is constructed for these wavelets. This matrix transforms the problem to a nonlinear system of algebraic equations. Solving the new system, enables one to identify the unknown coeffcients of expansion. Numerical results are compared with other existing methods to illustrate the applicability of the method.

Fourth kind Chebyshev wavelets, HIV model, Caputo derivative