Abstract and Applied Analysis

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1. J. S. Leszczynski, An Introduction to Fractional Mechanics, Czestochowa University of Technology, Częstochowa, Poland, 2011.
2. F. Mainardi, “Fractional calculus: some basic problems in continuum and statistical mechanics,” in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, Eds., pp. 291–348, Springer, New York, NY, USA, 1997. View at Google Scholar · View at Zentralblatt MATH
3. M. Caputo, “Linear models of dissipation whose Q is almost frequency independent-II,” Geophysical Journal of the Royal Astronomical Society, vol. 13, no. 5, pp. 529–539, 1967. View at Publisher · View at Google Scholar
4. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006.
5. R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, New Jersey, NJ, USA, 2000. View at Publisher · View at Google Scholar
6. R. L. Bagley and P. J. Torvik, “A theoretical basis for the application of fractional calculus,” Journal of Rheology, vol. 27, no. 3, pp. 201–210, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
7. R. L. Bagley and R. A. Calico, “Calico. Fractional order state equations for the control of viscoelastically damped structures,” Journal of Guidance, Control, and Dynamics, vol. 14, no. 2, pp. 304–311, 1991. View at Publisher · View at Google Scholar
8. E. J. S. Solteiro Pires, J. A. T. Machado, and P. B. de Moura Oliveira, “Fractional order dynamics in a GA planner,” Signal Processing, vol. 83, no. 11, pp. 2377–2386, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
9. K. S. Hedrih and V. N. Stanojevi, “A model of gear transmission: fractional order system dynamics,” Mathematical Problems in Engineering, vol. 2010, Article ID 972873, 2010. View at Publisher · View at Google Scholar
10. J. Cao, C. Ma, H. Xie, and Z. Jiang, “Nonlinear dynamics of duffing system with fractional order damping,” Journal of Computational and Nonlinear Dynamics, vol. 5, no. 4, pp. 041012–041018, 2010. View at Publisher · View at Google Scholar
11. C. P. Li and G. Chen, “Chaos and hyperchaos in the fractional-order Rössler equations,” Physica A, vol. 341, no. 1–4, pp. 55–61, 2004. View at Publisher · View at Google Scholar
12. K. Moaddy, S. Momani, and I. Hashim, “Non-standard finite difference schemes for solving fractional–order Rössler chaotic and hyperchaotic system,,” Computers & Mathematics with Applications, vol. 61, no. 4, pp. 1209–1216, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
13. Z. Odibat, S. Momani, and V. S. Erturk, “Generalized differential transform method: application to differential equations of fractional order,” Applied Mathematics and Computation, vol. 197, no. 2, pp. 467–477, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
14. S. Momani and 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, vol. 220, no. 1-2, pp. 85–95, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
15. Z. Odibat and S. Momani, “A generalized differential transform method for linear partial differential equations of fractional order,” Applied Mathematics Letters, vol. 21, no. 2, pp. 194–199, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
16. V. S. Erturk, S. Momani, and Z. Odibat, “Application of generalized differential transform method to multi-order fractional differential equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 8, pp. 1642–1654, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
17. Z. Odibat, C. Bertelle, M. A. Aziz-Alaoui, and G. Duchamp, “A multi-step differential transform method and application to non-chaotic or chaotic systems,” Computers & Mathematics with Applications, vol. 59, no. 4, pp. 1462–1472, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
18. V. S. Ertürk, Z. Odibat, and S. Momani, “An approximate solution of a fractional order differential equation model of human T-cell lymphotropic virus I (HTLV-I) infection of CD4⁺ T-cells,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 996–1002, 2011. View at Publisher · View at Google Scholar
19. I. Podlubny, Fractional Differential Equations, vol. 198, Academic Press Inc., San Diego, CA, USA, 1999.
20. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
21. J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of fractional calculus,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1140–1153, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
22. O. E. Rössler, “An equation for continuous chaos,” Physics Letters A, vol. 57, no. 5, p. 397, 1976. View at Publisher · View at Google Scholar
23. O. E. Rössler, “An equation for hyperchaos,” Physics Letters A, vol. 71, no. 2-3, pp. 155–157, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH