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### Proyecciones (Antofagasta) vol.34 no.4 Antofagasta Dec. 2015

#### http://dx.doi.org/10.4067/S0716-09172015000400001

Proyecciones Journal of Mathematics Vol. 34, No 4, pp. 307-322, December 2015. Universidad Católica del Norte Antofagasta - Chile

The multi-step homotopy analysis method for solving fractional-order model for HIV infection of CD4+T cells

AH H. Handam

Al Al-Bayt University Jordan

Ajloun College Al-Balqa Applied University

M. Zurigat

Al Al-Bayt University

Jordan

ABSTRACT

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 ho-motopy 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.

Subjclass [2000] : 26A33, 34A34.

Keywords: Fractional-order, Caputo fractional derivative, multistep homotopy analysis, HIV infection, Differential equation.

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Ali H. Handam

Department of Mathematics

Al al-Bayt University P. O. Box: 130095

Al Mafraq

Jordan

e-mail : ali.handam@windowslive.com

Applied Science Department

Ajloun College Al-Balqa Applied University Ajloun 26816

Jordan

M. Zurigat

Department of Mathematics,

Al al-Bayt University P. O. Box: 130095

Al Mafraq

Jordan

e-mail : moh_zur@hotmail.com

Received : March 2015. Accepted : October 2015