Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Human T-cell Lymphotropic Virus I (HTLV-I) infection of CD4+ T-Cells is one of the causes of health problems and continues to be one of the significant health challenges. In this article, a multi-step differential transform method is implemented to give approximate solutions of fractional modle of HTLV-I infection of CD4+ T-cells. Numerical results are compared to those obtained by the fourth-order Runge-Kutta method in the case of intger-order derivatives. The suggested method is efficient as the Runge-Kutta method. Some plots are presented to show the reliability and simplicity of the method.
Czasopismo
Rocznik
Tom
Strony
171--180
Opis fizyczny
Bibliogr. 21 poz., wykr.
Twórcy
autor
- Department of Mathematics, Al Al-Bayt University, P.O. Box: 130095 Mafraq, Jordan
autor
- Department of Mathematics, Al-Balqa Applied University, Salt, Jordan
Bibliografia
- [1] N.I. Stilianakis, J. Seydel, Modeling the T-cell dynamics and pathogenesis of HTLV-I infection, Bull. Math. Biol. 61 (1999) 935–947.
- [2] Patricia Katri, Shigui Ruan, Dynamics of human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells, C. R. Biologies. 327 (2004) 1009–1016.
- [3] L. Wang, M.Y. Li, D. Kirschner, Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression, Math. Biosci. 179 (2002) 207–217.
- [4] L.M. Petrovic, D.T. Spasic, T.M. Atanackovic, On a mathematical model of a human root dentin, Dental Materials. 21 (2005) 125 128.
- [5] A. Gokdogan, M. Merdan, A multistage homotopy perturbation method for solving human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells model, Middle-East Journal of Scientific Research. 9 (4) (2011) 503-509.
- [6] X. Y. Shi, H. Gao, V. I. Lazouskaya, Q. Kang, Y. Jin, L.P. Wang, Viscous flow and colloid transport near air–water interface in a microchannel, Computers & Mathematics with Applications. 59 (7) (2010) 2290-2304.
- [7] A. Gokdogan, M. Merdan, A multistage homotopy perturbation method for solving human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells model, Middle-East Journal of Scientific Research. 9 (4) (2011) 503-509.
- [8] G. Barro, O. So, J. M. Ntaganda, B. Mampassi, B. Some, A numerical method for some nonlinear differential equation models in biology, Applied Mathematics and Computation. 200(1) (2008) 28-33.
- [9] A. M. Wazwaz, New solutions of distinct physical structures to high-dimensional nonlinear evolution equations, Applied Mathematics and Computation. 196(1) (2008) 363-370.
- [10] I. Hashim, M.S.H. Chowdhury, S. Mawa, On multistage homotopy-perturbation method applied to nonlinear biochemical reaction model, Chaos, Solitons & Fractals. 36(4) (2008) 823-827.
- [11] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
- [12] Z. Odibat, S. Momani, V.S. Ert¨urk, Generalized differential transform method: Application to differential equations of fractional order, Appl. Math. Comput. 197 (2008) 467–477.
- [13] S. Momani, Z. Odibat, A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor’s formula, Journal of Computational and Applied Mathematics. 220 (2008) 85–95.
- [14] Z. Odibat, S. Momani, A generalized differential transform method for linear partial differential equations of fractional order, Applied Mathematics Letters. 21 (2008) 194–199.
- [15] V.S. Ertürk, S. Momani, Z. Odibat, Application of generalized differential transform method to multi-order fractional differential equations, Communications in Nonlinear Science and Numerical Simulation. 13 (2008) 1642–1654.
- [16] Z. Odibat, C. Bertelle, M.A. Aziz-Alaoui, G. Duchamp, A multi-step differential transform method and application to non-chaotic or chaotic systems, Computers & Mathematics with Applications. 59(4) (2010) 1462-1472.
- [17] I. S. Jesus, J. A. Machado, J. B. Cunha, Fractional electrical impedances in botanical elements, Journal of Vibration and Control. 14 (2008) 1389-1402.
- [18] K. S. Cole, Electric conductance of biological systems, Proc Cold Spring Harbor Symp Quant. Biol, Cold Spring Harbor. New York (1993) 107-116.
- [19] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, (2006).
- [20] S. Das, Functional Fractional Calculus, Springer, (2011).
- [21] R.L. Magin, Fractional Calculus in Bioengineering, Begell House Publishers, (2006).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b347d313-048d-4559-8517-005fb2b8a28c
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