Existence of solutions for fractional differential inclusions with antiperiodic boundary conditions

Boundary Value Problems

Volumn 2009, Issue , 2009, Pages

  Ahmad, Bashir ^a   Otero Espinar, Victoria ^b  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^b UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68349123813     PISSN: 16872762     EISSN: 16872770     Source Type: Journal    
DOI: 10.1155/2009/625347     Document Type: Article

References (37)

1. 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.
2. B. Ahmad and S. Sivasundaram, "Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions," to appear in Dynamic Systems and Applications.
3. B. Ahmad and J. J. Nieto, "Existence results for a coupled system of nonlinear functional differential equation with three-point boundary value problem," preprint.
4. 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.
5. G. H. Erjaee and S. Momani, "Phase synchronization in fractional differential chaotic systems," Physics Letters A, vol. 372, no. 14, pp. 2350-2354, 2008.
6. V. Gafiychuk, B. Datsko, and V. Meleshko, "Mathematical modeling of time fractional reaction-diffusion systems," Journal of Computational and Applied Mathematics, vol. 220, no. 1-2, pp. 215-225, 2008.
7. R. W. Ibrahim and M. Darus, "Subordination and superordination for univalent solutions for fractional differential equations," Journal of Mathematical Analysis and Applications, vol. 345, no. 2, pp. 871-879, 2008.
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, Amsterdam, The Netherlands, 2006.
9. S. Ladaci, J. J. Loiseau, and A. Charef, "Fractional order adaptive high-gain controllers for a class of linear systems," Communications in Nonlinear Science and Numerical Simulation, vol. 13, no. 4, pp. 707-714, 2008.
10. α fractional control of robotic time-delay systems," Mechanics Research Communications, vol. 33, no. 2, pp. 269-279, 2006.
11. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, San Diego, Calif, USA, 1999.
12. S. Z. Rida, H. M. El-Sherbiny, and A. A. M. Arafa, "On the solution of the fractional nonlinear Schrödinger equation," Physics Letters A, vol. 372, no. 5, pp. 553-558, 2008.
13. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, Switzerland, 1993.
14. S. Zhang, "Existences of solutions for a boundary value problem of fractional order," Acta Mathematica Scientia, vol. 26, no. 2, pp. 220-228, 2006.
15. B. Ahmad and J. J. Nieto, "Existence and approximation of solutions for a class of nonlinear impulsive functional differential equations with anti-periodic boundary conditions," Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 10, pp. 3291-3298, 2008.
16. B. Ahmad and J. J. Nieto, "Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree," preprint.
17. Y. Chen, J. J. Nieto, and D. O'Regan, "Anti-periodic solutions for fully nonlinear first-order differential equations," Mathematical and Computer Modelling, vol. 46, no. 9-10, pp. 1183-1190, 2007.
18. D. Franco, J. J. Nieto, and D. O'Regan, "Anti-periodic boundary value problem for nonlinear first order ordinary differential equations," Mathematical Inequalities & Applications, vol. 6, no. 3, pp. 477-485, 2003.
19. D. Franco, J. J. Nieto, and D. O'Regan, "Existence of solutions for first order ordinary differential equations with nonlinear boundary conditions," Applied Mathematics and Computation, vol. 153, no. 3, pp. 793-802, 2004.
20. B. Liu, "An anti-periodic LaSalle oscillation theorem for a class of functional differential equations," Journal of Computational and Applied Mathematics, vol. 223, no. 2, pp. 1081-1086, 2009.
21. Z. Luo, J. Shen, and J. J. Nieto, "Antiperiodic boundary value problem for first-order impulsive ordinary differential equations," Computers & Mathematics with Applications, vol. 49, no. 2-3, pp. 253-261, 2005.
22. K. Wang and Y. Li, "A note on existence of (anti-)periodic and heteroclinic solutions for a class of second-order odes," Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 4, pp. 1711-1724, 2009.
23. S. Abbasbandy, J. J. Nieto, and M. Alavi, "Tuning of reachable set in one dimensional fuzzy differential inclusions," Chaos, Solitons & Fractals, vol. 26, no. 5, pp. 1337-1341, 2005.
24. Y.-K. Chang, W.-T. Li, and J. J. Nieto, "Controllability of evolution differential inclusions in Banach spaces," Nonlinear Analysis: Theory, Methods & Applications, vol. 67, no. 2, pp. 623-632, 2007.
25. M. Frigon, "Systems of first order differential inclusions with maximal monotone terms," Nonlinear Analysis: Theory, Methods & Applications, vol. 66, no. 9, pp. 2064-2077, 2007.
26. J. J. Nieto and R. Rodríguez-López, "Euler polygonal method for metric dynamical systems," Information Sciences, vol. 177, no. 20, pp. 4256-4270, 2007.
27. G. V. Smirnov, Introduction to the Theory of Differential Inclusions, vol. 41 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 2002.
28. Y.-K. Chang and J. J. Nieto, "Existence of solutions for impulsive neutral integrodi-differential inclusions with nonlocal initial conditions via fractional operators," Numerical Functional Analysis and Optimization, vol. 30, no. 3-4, pp. 227-244, 2009.
29. Y.-K. Chang, J. J. Nieto, and W.-S. Li, "On impulsive hyperbolic differential inclusions with nonlocal initial conditions," Journal of Optimization Theory and Applications, vol. 140, no. 3, pp. 431-442, 2009.
30. J. Henderson and A. Ouahab, "Fractional functional differential inclusions with finite delay," Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 5, pp. 2091-2105, 2009.
31. W.-S. Li, Y.-K. Chang, and J. J. Nieto, "Existence results for impulsive neutral evolution differential inclusions with state-dependent delay," Mathematical and Computer Modelling, vol. 49, no. 9-10, pp. 1920-1927, 2009.
32. A. Ouahab, "Some results for fractional boundary value problem of differential inclusions," Nonlinear Analysis: Theory, Methods & Applications, vol. 69, no. 11, pp. 3877-3896, 2008.
33. 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.
34. K. Deimling, Multivalued Differential Equations, vol. 1 of de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter, Berlin, Germany, 1992.
35. S. Hu and N. Papageorgiou, Handbook of Multivalued Analysis, Theory Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1997.
36. H. F. Bohnenblust and S. Karlin, "On a theorem of Ville," in Contributions to the Theory of Games. Vol. I, Annals of Mathematics Studies, no. 24, pp. 155-160, Princeton University Press, Princeton, NJ, USA, 1950.
37. A. Lasota and Z. Opial, "An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations," Bulletin de l'Académie Polonaise des Sciences. Série des Sciences Mathématiques, Astronomiques et Physiques, vol. 13, pp. 781-786, 1965.