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International Journal of Differential Equations
Volume 2010 (2010), Article ID 509286, 9 pages
The Periodic Solutions of the Compound Singular Fractional Differential System with Delay
School of Mathematics and Computer Science, Fuzhou Universiy, Fuzhou 350108, China
Received 31 July 2009; Revised 16 November 2009; Accepted 1 December 2009
Academic Editor: Fawang Liu
Copyright © 2010 XuTing Wei and XuanZhu Lu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, London, UK, 1999.
- K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, New York, NY, USA, 1993.
- Xuanzhu Lu and Fawang Liu, “The explicit and implicit finite difference approximations for the space fractional advection diffusion equation,” Computational Mechanics, September 2004, Beijing, China.
- A. Arikoglu and I. Ozkol, “Solution of fractional differential equations by using differential transform method,” Chaos, Solitons and Fractals, vol. 34, no. 5, pp. 1473–1481, 2007.
- M. M. Meerschaert, “Stochastic solution of space-time fractional diffusion equations,” Physical Review E, vol. 65, no. 4, Article ID 041103, 4 pages, 2002.
- F. Liu, V. V. Anh, and I. Turner, “Time fractional advection-dispersion equation,” Journal of Applied Mathematics & Computing, vol. 13, no. 1-2, pp. 233–245, 2003.
- M. Unser and T. Blu, “Fractional splines and wavelets,” SIAM Journal, vol. 42, no. 1, pp. 43–67, 2000.
- P. Varshney, M. Gupta, and G. S. Visweswaran, “New switched capacitor fractional order integrator,” Journal of Active and Passive Electronic Devices, pp. 187–197, 2007.
- T.-M. Hsieh, S.-D. Lin, and H. M. Srivastava, “Some relationships between certain families of ordinary and fractional differential equations,” Computers and Mathematics with Applications, vol. 46, no. 10-11, pp. 1483–1492, 2003.
- K. Nishimoto, Fractional Calculus: Integrations and Differentiations of Arbitrary Order, vol. 1, Descartes Press, Koriyama, Japan, 1984.
- M. L. Hbid and R. Qesmi, “Periodic solutions for functional differential equations with periodic delay close to zero,” Electronic Journal of Differential Equations, vol. 141, pp. 1–12, 2006.
- Z.-X. Zhang and W. Jiang, “The periodic solution of compound singular differential equation with delay,” Journal of Anhui University Natural Science Edition, vol. 30, pp. 4–7, 2006.
- V. Kevantuo and C. Lizama, “A characterization of periodic solutions for time-fractional differential equations in UMD spaces and applications,” Mathematische Nachrichten, pp. 25–28, 2008.
- J. L. Kaplan and J. A. Yorke, “Ordinary differential equations which yield periodic solutions of differential delay equations,” Journal of Mathematical Analysis and Applications, vol. 48, pp. 317–324, 1993.
- W. Deng, C. Li, and J. Lü, “Stability analysis of linear fractional differential system with multiple time delays,” Nonlinear Dynamics, vol. 48, no. 4, pp. 409–416, 2007.