Stability analysis for fractional differential equations and their applications in the models of HIV-I infection

CMES - Computer Modeling in Engineering and Sciences

Volumn 39, Issue 3, 2009, Pages 301-317

  Kou, Chunhai ^a   Yan, Ye ^a   Liu, Jian ^a  

^a DONGHUA UNIVERSITY   (China)

Author keywords

Equilibrium; Fractional differential equation; Model of HIV; Stability

Indexed keywords

DIFFERENTIAL EQUATIONS; STABILITY;

EQUILIBRIUM; FRACTIONAL DIFFERENTIAL EQUATION; FRACTIONAL ORDERS; STABILITY ANALYSIS; STABILITY OF EQUILIBRIUM;

MATHEMATICAL MODELS;

EID: 63349102926     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. Ahmed, E.; Elgazzar, A. S.; Hegazi, A. S. (2008): Modeling the avian flu, lessons form complex adaptive systems in biology. Appl. Math. Compt., vol. 195, pp. 351-354.
2. Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A. (2007): Equilibrium points, stability qnd numerical solutions of fractional-order predator-prey and rabies models. J. Math. Anal. Appl., vol. 325, pp. 542-553.
3. Ahmed, E.; Elgazzar, A. S. (2007): On fractional order differential equations model for nonlocal epidemics. Physica A, vol. 379, pp. 607-614.
4. Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A. (2004): On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rössler, Chua, and Chen systems. Physics Letters A, vol. 358, pp. 1-4.
5. Bagley, R. L. (1983): A theoretical basis for the application of fractional calculus to viscoelasticity. Journal of Rheology, vol. 27, pp. 201-210.
6. Caputo, M. (1967): Linear models of dissipation whose Q is almost independent, II. Geophy. J. Roy. Astraunom., vol. 13, pp. 529-539.
7. Chen, Z.; Gan, Y.; Chen, J. K. (2008): A Coupled Thermo-MechanicalModel for Simulating the Material Failure Evolution Due to Localized Heating. CMES: Computer Modeling in Engineering & Sciences, vol. 26, pp. 123-137.
8. De Leenheer, P.; Smith, H. L. (2003): Virus dynamics: A global analysis. SIAM J. Appl. Math., vol. 63, pp. 1313-1327.
9. Hilfer, R. (ed) (2001): Applications of fractional calculus in physics. World Scientific, New Jersey.
10. Ichise, M.; Nagayanagi, Y.; Kojima, T. (1971): An analog simulation of noninteger order transfer function for analysis of electrode process. J. Electroanal Chem., vol. 33, pp. 253-265.
11. Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J. (2006): Theory and Applications of fractional differential equations. North-Holland Mathematics Studies 204, Elsvier, Amsterdam.
12. Koller, R. C. (1984): Application of fractional calculus to the theory of viscoelasticity. J. Appl. Mech., vol. 51, pp. 299-307.
13. Kouche, M.; Ainseba, B. (2007(to appear)): A mathematical model of HIV-I infection in tissue culture. Discrete and Continuous Dynamical System, Supplement volume.
14. Lu, Y. Y.; Zhu, J. X. (2007): Perfectlymatched layer for acoustic waveguide modelings benchmark calculations and perturbation analysis. CMES: Computer Modeling in Engineering & Sciences, vol. 22, pp. 235-247.
15. Matignon, D. (1996): Stability results for fractional differential equations with applications to control processing. Computational Engineering in System Application, Lille, France, pp. 963-968.
16. Metzler, R.; Schick, W.; Kilian, H. G.; Nonnenma-cher, T. F. (1995): Relaxation in filled polymers: A fractional calculus approach. J. Chem. Phys., vol. 103, pp. 7180-7186.
17. Nishidate, Y.; Nikishkov, G. P. (2008): Atomic-scaleModeling of Self-Positioning Nanostructures. CMES: Computer Modeling in Engineering & Sciences, vol. 26, pp. 91-106.
18. Perelson, A. S. (1989): Modelling the interaction of the immune system with HIV. Mathematical and Statistical Approaches to AIDS Epidemiology(ed. C. Castillo-Chavez), Springer-Verlag, New York, pp. 350-370.
19. + T-cells. Math. Biosc., vol. 114, pp. 81-125.
20. Shan, Y. Y.; Shu, C.; Lu, Z. L. (2008): Application of Local MQ-DQ Method to Solve 3D Incompressible Viscous Flows with Curved Boundary. CMES: Computer Modeling in Engineering & Sciences, vol. 25, pp. 99-113.
21. Spouge, J. L.; Shrager, R. L; Dimitrov, D. S. (1996): HIV-I infection kinetics in tissue cultures. Math. Biosc, vol. 138, pp. 1-22.