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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 532589, 8 pages
Uniform Asymptotic Stability of Solutions of Fractional Functional Differential Equations
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
Received 30 September 2013; Accepted 15 October 2013
Academic Editor: Massimiliano Ferrara
Copyright © 2013 Yajing Li and Yejuan Wang. 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.
- T. Caraballo, P. Marín-Rubio, and J. Valero, “Autonomous and non-autonomous attractors for differential equations with delays,” Journal of Differential Equations, vol. 208, no. 1, pp. 9–41, 2005.
- J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, Springer, New York, NY, USA, 1993.
- Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1993.
- M. C. Mackey and L. Glass, “Oscillation and chaos in physiological control systems,” Science, vol. 197, pp. 287–289, 1977.
- M. Benchohra, J. Henderson, S. K. Ntouyas, and A. Ouahab, “Existence results for fractional order functional differential equations with infinite delay,” Journal of Mathematical Analysis and Applications, vol. 338, no. 2, pp. 1340–1350, 2008.
- M. Benchohra and B. A. Slimani, “Partial neutral functional hyperbolic differential equations with Caputo fractional derivative,” Nonlinear Analysis Forum, vol. 15, pp. 143–151, 2010.
- K. Diethelm and N. J. Ford, “Analysis of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 265, no. 2, pp. 229–248, 2002.
- K. Diethelm, The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo Type, vol. 2004 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2010.
- A. A. Kilbas and J. J. Trujillo, “Differential equations of fractional order: methods, results and problems. II,” Applicable Analysis, vol. 81, no. 2, pp. 435–493, 2002.
- S. A. Messaoudi, B. Said-Houari, and N. Tatar, “Global existence and asymptotic behavior for a fractional differential equation,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1955–1962, 2007.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
- F. Chen and Y. Zhou, “Attractivity of fractional functional differential equations,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1359–1369, 2011.
- F. Chen, J. J. Nieto, and Y. Zhou, “Global attractivity for nonlinear fractional differential equations,” Nonlinear Analysis. Real World Applications, vol. 13, no. 1, pp. 287–298, 2012.
- B. C. Dhage, “Local asymptotic attractivity for nonlinear quadratic functional integral equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 5, pp. 1912–1922, 2009.
- B. C. Dhage, “Global attractivity results for nonlinear functional integral equations via a Krasnoselskii type fixed point theorem,” Nonlinear Analysis. Theory, Methods & Applications, vol. 70, no. 7, pp. 2485–2493, 2009.
- B. C. Dhage and V. Lakshmikantham, “On global existence and attractivity results for nonlinear functional integral equations,” Nonlinear Analysis. Theory, Methods & Applications, vol. 72, no. 5, pp. 2219–2227, 2010.
- J. Banaś and B. C. Dhage, “Global asymptotic stability of solutions of a functional integral equation,” Nonlinear Analysis. Theory, Methods & Applications, vol. 69, no. 7, pp. 1945–1952, 2008.
- D. Henry, Geometric Theory of Semilinear Parabolic Partial Differential Equations, Springer, Berlin, Germany, 1989.
- W. H. Deng, “Numerical algorithm for the time fractional Fokker-Planck equation,” Journal of Computational Physics, vol. 227, no. 2, pp. 1510–1522, 2007.