Existence of periodic solution for a nonlinear fractional differential equation

Boundary Value Problems

Volumn 2009, Issue , 2009, Pages

  Belmekki, Mohammed ^a   Nieto, Juan J ^b   Rodríguez López, Rosana ^b  

^a UNIVERSITY OF SAIDA   (Algeria)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70249121999     PISSN: 16872762     EISSN: 16872770     Source Type: Journal    
DOI: 10.1155/2009/324561     Document Type: Article

References (26)

1. B. Ahmad and J. J. Nieto, "Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions," preprint.
2. B. Ahmad and J. J. Nieto, "Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions," Boundary Value Problems, vol. 2009, Article ID 708576, 11 pages, 2009.
3. M. Benchohra, A. Cabada, and D. Seba, "An existence result for nonlinear fractional differential equations on Banach spaces," Boundary Value Problems, vol. 2009, Article ID 628916, 11 pages, 2009.
4. B. Bonilla, M. Rivero, L. Rodríguez-Germá, and J. J. Trujillo, "Fractional differential equations as alternative models to nonlinear differential equations," Applied Mathematics and Computation, vol. 187, no. 1, pp. 79-88, 2007.
5. V. Daftardar-Gejji and S. Bhalekar, "Boundary value problems for multi-term fractional differential equations," Journal of Mathematical Analysis and Applications, vol. 345, no. 2, pp. 754-765, 2008.
6. V. Varlamov, "Differential and integral relations involving fractional derivatives of Airy functions and applications," Journal of Mathematical Analysis and Applications, vol. 348, no. 1, pp. 101-115, 2008.
7. M. P. Lazarević and A. M. Spasić, "Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach," Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 475-481, 2009.
8. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam, The Netherlands, 2006.
9. V. Kiryakova, Generalized Fractional Calculus and Applications, vol. 301 of Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow, UK, 1994.
10. K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, A Wiley-Interscience Publication, JohnWiley & Sons, New York, NY, USA, 1993.
11. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
12. K. B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, NY, USA, 1974.
13. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science, Yverdon, Switzerland, 1993.
14. K. Diethelm and A.D. Freed, "On the solution of nonlinear fractional order differential equations used in the modeling of viscoplasticity," in Scientifice Computing in Chemical Engineering II-Computational Fluid Dynamics, Reaction Engineering and Molecular Properties, F. Keil, W. Mackens, H. Voss, and J. Werther, Eds., pp. 217-224, Springer, Heidelberg, Germany, 1999.
15. 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.
16. K. Diethelm and G. Walz, "Numerical solution of fractional order differential equations by extrapolation," Numerical Algorithms, vol. 16, no. 3-4, pp. 231-253, 1997.
17. F. Mainardi, "Fractional calculus: Some basic problems in continuum and statistical mechanis," in Fractals and Fractional Calculus in Continuum Mechanics, A. Carpinteri and F. Mainardi, Eds., pp. 291-348, Springer, Wien, Austria, 1997.
18. R. Metzler, W. Schick, H.-G. Kilian, and T. F. Nonnenmacher, "Relaxation in filled polymers: A fractional calculus approach," The Journal of Chemical Physics, vol. 103, no. 16, pp. 7180-7186, 1995.
19. I. Podlubny, I. Petráš, B. M. Vinagre, P. O'Leary, and L. Dorčák, "Analogue realizations of fractionalorder controllers," Nonlinear Dynamics, vol. 29, no. 1-4, pp. 281-296, 2002.
20. D. Araya and C. Lizama, "Almost automorphic mild solutions to fractional differential equations," Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 11, pp. 3692-3705, 2008.
21. M. Benchohra, S. Hamani, J. J. Nieto, and B. A. Slimani, "Existence results for fractional differential inclusions with fractional order and impulses," to appear in Computers & Mathematics with Applications.
22. Y.-K. Chang and J. J. Nieto, "Some new existence results for fractional differential inclusions with boundary conditions," Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 605-609, 2009.
23. Y.-K. Chang and J. J. Nieto, "Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators," Numerical Functional Analysis and Optimization, vol. 30, pp. 227-244, 2009.
24. H. Jafari and S. Seifi, "Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation," Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 5, pp. 2006-2012, 2009.
25. J. Li, J. J. Nieto, and J. Shen, "Impulsive periodic boundary value problems of first-order differential equations," Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 226-236, 2007.
26. J. J. Nieto, "Differential inequalities for functional perturbations of first-order ordinary differential equations," Applied Mathematics Letters, vol. 15, no. 2, pp. 173-179, 2002.