طالعه یک مدل مرتبه کسری برای بررسی اثر درمان دارویی بر کنترل اچ‌آی‌وی

[1] K. Alcorn, A. Poppa and M. Nicholson, HIV and AIDS Treatments Directory, NAM, (1999).
[2] R. Goldsby, T. Kiudt, B. Osborae and J. Kuby, Immunology, New York, (2003).
[3] M. Sande and P. Volberding, The Medical Management of AIDS, (No. Ed. 4), WB Saunders (1999).
[4] C. M. Pinto and A. R. Carvalho, A latency fractional order model for HIV dynamics, J. Comput. Appl. Math., 312 (2017) 240–256.
[5] X. Zhou, X. Song and X. Shi, A differential equation model of HIV infection of CD4+ T -cells with cure rate, J. Math. Anal. Appl., 342 (2008) 1342–1355.
[6] A. S. Perelson, Modeling the interaction of the immune system with HIV, Mathematical and Statistical Approaches to AIDS Epidemiology, Lecture Notes in Biomath., 83, Springer, Berlin, 1989 350–370.
[7] A. S. Perelson, D. E. Kirschner and R. De Boer, Dynamics of HIV infection of CD4+ T -cells, Math. Biosci., 114 (1993) 81–125.
[8] L. Wang and M. Y. Li, Mathematical analysis of the global dynamics of a model for HIV infection of CD4+T -cells, Math. Biosci., 200 (2006) 44–57.

[9] R. V. Culshaw and S. Ruan, A delay-differential equation model of HIV infection of cells, Mathematical Biosciences, 165 (2000) 27–39
[10] A . S. Perelson, A. U. Neumann, M. Markowitz, J. M. Leonard and D. D. Ho, HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span and viral generation time, Science, 271 (1996) 1582–1586.
[11] P. W. Nelson and A. S. Perelson, Mathematical analysis of delay differential equation models of HIV-1 infection, Math. Biosci., 179 (2002) 73–94.
[12] Y. Zhou, Basic theory of fractional differential equations, World Scientific Publishing, Co. Pte. Ltd., Hackensack, NJ, 2014.
[13] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, 204, Elsevier Science B.V., Amsterdam, 2006.
[14] K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1993.
[15] A. Oustaloup, La derivation non entiere: theorie, Synthese et Applications, (Non-Integer Derivation: Theory, Synthesis and Applications), Editions Hermes, Paris, 1995.
[16] R. W. Ibrahim and S. Momani, On the existence and uniqueness of solutions of a class of fractional differential equations, J. Math. Anal. Appl., 334 (2007) 1–10.
[17] Y. Li, T. Q. Chen and I. Podlubny, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability, Comput. Math. Appl., 59 (2010) 1810–1821.
[18] M. Stojanovic, Existence-uniqueness result for a nonlinear n-term fractional equation, J. Math. Anal. Appl., 353 (2009) 244–255.
[19] Hilfer, R. (Ed.). (2000). Applications of Fractional Calculus in Physics (Vol. 35, No. 12, pp. 1200–1205), Singapore: world scientific.
[20] S. Abbas, M. Benchohra, G. M. N’Gurkata and B. A. Slimani, Darboux problem for fractional-order discontinuous hyperbolic partial differential equations in Banach algebras, Complex Var. Elliptic Equ., 57 (2012) 337–350.
[21] A. R. M. Carvalho and C. M. A. Pinto, Emergence of drug-resistance in HIV dynamics under distinct HAART regimes, Commun. Nonlinear Sci. Numer. Simul., 30 (2016) 207–226.
[22] Y. Ding and H. Ye, A fractional-order differential equation model of HIV infection of CD4+ T-cells., Math. Comput. Modelling, 50 (2009) 386–392.
[23] H. Ye and Y. Ding, Nonlinear dynamics and chaos in a fractional-order HIV model, Mathematical Problems in Engineering, 2009 (2009) 1–12.
[24] K. Diethelm, N. J. Ford, A. D. Freed and Y. Luchko, Algorithms for the fractional calculus: a selection of numerical methods, Comput. Methods Appl. Mech. Engrg., 194 (2005) 743–773.
[25] D. Kirschner, S. Lenhart and S. Serbin, Optimal control of the chemotherapy of HIV, J. Math. Biol., 35 (1997) 775–792.
[26] Z. M. Odibat and N. T. Shawagfeh, Generalized Taylor’s formula, Appl. Math. Comput., 186 (2007) 286–293.
[27] W. Lin, Global existence theory and chaos control of fractional differential equations, J. Math. Anal. Appl., 332 (2007) 709–726.
[28] P. Van Den Driessche and P. Watmough, Reprodoction numbers and subthreshold endemic equilibria for com-partmental models of disease transmission, Math. Biosci., 180 (2002) 29–48.

[29] A. G. Radwan, K. Moaddy and S. Momani, Stability and non-standard finite difference method of the generalized Chua’s circuit, Comput. Math. Appl., 62 (2011) 961–970.
[30] C. H. Kou, Y. Yan and J. Liu, Stability analysis for fractional differential equations and their applications in the models of HIV-1 infection, CMES Comput. Model. Eng. Sci., 39 (2009) 301–317.
[31] E. Ahmed, A. M. A. El-Sayed and H. A. A. El-Saka, On some Routh-Hurwitz conditions for fractional differential equations and their applications in Lorenz, Rossler, Chua and Chen systems, Phys. Lett. A, 358 (2006) 1–4.
[32] K. Diethelm, N. J. Ford and A. D. Freed, A predictor-corrector approach for the numerical solution of fractional differentional equations, Nonlinear Dynam., 29 (2002) 3–22.