Analytic study for a fractional model of HIV infection of C D 4 + T lymphocyte cells

In this article, we implemented homotopy transform methods, namely, homotopy analysis transform method and homotopy perturbation Sumudu transform method to examine the fractional model for HIV infection of CD4+T lymphocyte cells. Proliferation of CD4+T lymphocyte cells is driven by a combination of the homeostatic response to cells depletion (CD4+T cells counts) and viral load (HIV levels). The attraction of both the methods is that an approach of HPSTM is used and on other hand by HATM a large admissible convergence range of series solution is described for standard as well as fractional order nonlinear problems.

[1]  Devendra Kumar,et al.  Homotopy Perturbation Method for Fractional Gas Dynamics Equation Using Sumudu Transform , 2013 .

[2]  Adem Kilicman,et al.  Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations , 2014 .

[3]  Vineet K. Srivastava,et al.  Numerical approximation for HIV infection of CD4+ T cells mathematical model , 2014 .

[4]  E. Ahmed,et al.  Equilibrium points, stability and numerical solutions of fractional-order predator–prey and rabies models , 2007 .

[5]  Shijun Liao Do peaked solitary water waves indeed exist? , 2014, Commun. Nonlinear Sci. Numer. Simul..

[6]  F. Belgacem,et al.  Towards a Sumudu based estimation of large scale disasters environmental fitness changes adversely affecting population dispersal and persistence , 2014 .

[7]  Devendra Kumar,et al.  Numerical study for systems of fractional differential equations via Laplace transform , 2015 .

[8]  N. Doğan,et al.  Numerical Treatment of the Model for HIV Infection of CD4 , 2012 .

[9]  Ji-Huan He,et al.  Homotopy perturbation method: a new nonlinear analytical technique , 2003, Appl. Math. Comput..

[10]  S. Liao,et al.  Beyond Perturbation: Introduction to the Homotopy Analysis Method , 2003 .

[11]  Devendra Kumar,et al.  Numerical computation of fractional Lotka-Volterra equation arising in biological systems , 2015 .

[12]  Adam Grabowski,et al.  Introduction to the Homotopy Theory , 1997 .

[13]  Devendra Kumar,et al.  A Reliable Algorithm for a Local Fractional Tricomi Equation Arising in Fractal Transonic Flow , 2016, Entropy.

[14]  S. Schreiber,et al.  Prevention of HIV-1 infection and preservation of CD4 function by the binding of CPFs to gp120. , 1990, Science.

[15]  S. Schwartz,et al.  Current Concepts in Human Immunodeficiency Virus Infection and AIDS , 1999, Clinical Diagnostic Laboratory Immunology.

[16]  G. K. Watugala,et al.  Sumudu Transform - a New Integral Transform to Solve Differential Equations and Control Engineering Problems , 1992 .

[17]  Shyam L. Kalla,et al.  ANALYTICAL INVESTIGATIONS OF THE SUMUDU TRANSFORM AND APPLICATIONS TO INTEGRAL PRODUCTION EQUATIONS , 2003 .

[18]  Ş. Yüzbaşı A numerical approach to solve the model for HIV infection of CD4+T cells , 2012 .

[19]  Devendra Kumar,et al.  Fractional modelling arising in unidirectional propagation of long waves in dispersive media , 2016 .

[20]  Ji-Huan He Homotopy perturbation technique , 1999 .

[21]  Shijun Liao,et al.  On the steady-state fully resonant progressive waves in water of finite depth , 2012, Journal of Fluid Mechanics.

[22]  Shijun Liao,et al.  Homotopy Analysis Method in Nonlinear Differential Equations , 2012 .

[23]  Michael Y. Li,et al.  Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells. , 2006, Mathematical biosciences.

[24]  Abdon Atangana,et al.  Solving a system of fractional partial differential equations arising in the model of HIV infection of CD4+ cells and attractor one-dimensional Keller-Segel equations , 2013 .

[25]  Haci Mehmet Baskonus,et al.  Active Control of a Chaotic Fractional Order Economic System , 2015, Entropy.

[26]  Ji-Huan He New interpretation of homotopy perturbation method , 2006 .

[27]  Iqtadar Hussain,et al.  A new comparative study between homotopy analysis transform method and homotopy perturbation transform method on a semi infinite domain , 2012, Math. Comput. Model..

[28]  Saad Zagloul Rida,et al.  GENERAL: Exact Solutions of Fractional-Order Biological Population Model , 2009 .

[29]  Hasan Bulut,et al.  On the numerical solutions of some fractional ordinary differential equations by fractional Adams-Bashforth-Moulton method , 2015 .

[30]  Mevlüde Yakit Ongun,et al.  The Laplace Adomian Decomposition Method for solving a model for HIV infection of CD4+T cells , 2011, Math. Comput. Model..

[31]  Fethi Bin Muhammad Belgacem,et al.  Extraction of the Laplace, Fourier, and Mellin transforms from the Sumudu transform , 2014 .

[32]  Adem Kilicman,et al.  An Efficient Approach for Fractional Harry Dym Equation by Using Sumudu Transform , 2013 .

[33]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .