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

• Handam, Alí H. ^[1] ; Freihat, Asad A. ^[2] ; Zurigat, Mohammad ^[1]
  1. [1] Al al-Bayt University

     Al al-Bayt University

     Jordania

     
  2. [2] Al-Balqa` Applied University

     Al-Balqa` Applied University

     Jordania

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 34, Nº. 4, 2015, págs. 307-322
• Idioma: inglés
• DOI: 10.4067/S0716-09172015000400001
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • Citas [1] A. K. Alomari, M. S. M. Noorani, R. Nazar, C. P. Li, Homotopy analysis method for solving fractional Lorenz system, Commun Nonliear...
  • [2] J. Cang, Y. Tan, H. Xu, S. Liao, Series solutions of non-linear Riccati differential equations with fractional order, Chaos, Solitons...
  • [3] R.V. Culshaw, S. Ruan, A delay-differential equation model of HIV infection of CD4+ T-cells, Mathematical Bioscience 165, pp. 27-39,...
  • [4] Y. Ding, H. Ye, A fractional-order differential equation model of HIV infection of CD4+ T-cells, Mathematical and Computer Modelling,...
  • [5] V. S. Ert¨urk, Z. Odibat, S. Momani, An approximate solution of a fractional order differential equation model of human T-cell lymphotropic...
  • [6] C.P. Li, W.H. Deng, Remarks on fractional derivatives, Applied Mathematics and Computation 187, pp. 777—784, (2007).
  • [7] W. Lin, Global existence theory and chaos control of fractional differential equations, JMAA, 332, pp. 709-726, (2007).
  • [8] M. Merdan, homotopy perturbation method for solving a model for HIV infection of T-cells. Istanbul Ticaret Universitesi Fen Bilimleri...
  • [9] S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, USA, (1993).
  • [10] K. B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York, (1974).
  • [11] M. A. Nowak, R. M. May, Virus Dynamics, Oxford University Press, (2000).
  • [12] A.S. Perelson, Modelling the interaction of the immune system with HIV, in: C. Castillo-Chavez (Ed.), Mathematical and Statistical Approaches...
  • [13] A. S. Perelson, D. E. Kirschner, R. De Boer, Dynamics of HIV infection of CD4+ T-cells, Math. Biosci, 114 (1), pp. 81-125, (1993).
  • [14] A.S. Perelson, P.W. Nelson, Mathematical analysis of HIV-1, dynamics in vivo, SIAM Rev. 41 (1), pp. 3-44, (1999).
  • [15] I. Podlubny, Fractional Differential Equations. Academic Press, New York, (1999).
  • [16] A. Rafiq, M. Rafiullah, Some multi-step iterative methods for solving nonlinear equations, Computers & Mathematics with Applications,...
  • [17] J. Sabatier, O .P. Agrawal, J. A. Tenreiro Machado, Advances in Fractional Calculus; Theoretical Developments and Applications in Physics...
  • [18] M. Zurigat, S. Momani, Z. odibat, A. Alawneh, The homotopy analysis method for handling systems of fractional differential equations,...
  • [19] M. Zurigat, S. Momani, A. Alawneh, Analytical approximate solutions of systems of fractional algebraic-differential equations by homotopy...