Ali H. Handam, Asad A. Freihat and Mohammad Zurigat, The multi-step homotopy analysis method for solving fractional-order model for HIV infection of CD4+ T cells, Proyecciones Journal of Mathematics, 34 (4) (2015), 307-322.

HIV infection of CD4+T cells is one of the causes of health problems and continues to be one of the significant health challenges. This paper presents approximate analytical solutions to the model of HIV infection of CD4+T cells of fractional order using the multi-step homotopy analysis method (MHAM). The proposed scheme is only a simple modification of the homotopy analysis method (HAM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. The fractional derivatives are described in the Caputo sense. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically.