Existence results for fractional differential inclusions with separated boundary conditions

Bulletin of the Korean Mathematical Society

Volumn 47, Issue 4, 2010, Pages 805-813

  Ahmad, Bashir ^a  

^a KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

Author keywords

Bohnenblust Karlins fixed point theorem; Fractional differential inclusions; Separated boundary conditions

Indexed keywords

EID: 77958541432     PISSN: 10158634     EISSN: None     Source Type: Journal    
DOI: 10.4134/BKMS.2010.47.4.805     Document Type: Article

References (26)

1. B. Ahmad and J. J. Nieto, Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions, Bound. Value Probl. 2009, Art. ID 708576, 11 pp.
2. B. Ahmad and J. J. Nieto, Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions, Comput. Math. Appl. 58 (2009), no. 9, 1838-1843.
3. B. Ahmad and J. J. Nieto, Existence results for nonlinear impulsive hybrid boundary value problems involving fractional differential equations, Nonlinear Anal. Hybrid Syst. 3 (2009), no. 3, 251-258.
4. B. Ahmad and S. Sivasundaram, Existence and uniqueness results for nonlinear boundary value problems of fractional differential equations with separated boundary conditions, Commun. Appl. Anal. 13 (2009), no. 1, 121-127.
5. H. F. Bohnenblust and S. Karlin, On a theorem of Ville, Contributions to the Theory of Games, 155-160. Annals of Mathematics Studies, no. 24. Princeton University Press, Princeton, N. J., 1950.
6. Y.-K. Chang, W. T. Li, and J. J. Nieto, Controllability of evolution differential inclusions in Banach spaces, Nonlinear Anal. 67 (2007), no. 2, 623-632.
7. Y.-K. Chang and J. J. Nieto, Some new existence results for fractional differential inclusions with boundary conditions, Math. Comput. Modelling 49 (2009), no. 3-4, 605-609.
8. Y.-K. Chang and J. J. Nieto, Existence of solutions for impulsive neutral integro-differential inclusions with nonlocal initial conditions via fractional operators, Numer. Funct. Anal. Optim. 30 (2009), no. 3-4, 227-244.
9. Y.-K. Chang, J. J. Nieto, and W. S. Li, On impulsive hyperbolic differential inclusions with nonlocal initial conditions, J. Optim. Theory Appl. 140 (2009), no. 3, 431-442.
10. V. Daftardar-Gejji and S. Bhalekar, Boundary value problems for multi-term fractional differential equations, J. Math. Anal. Appl. 345 (2008), no. 2, 754-765.
11. K. Deimling, Multivalued Differential Equations, Walter de Gruyter & Co., Berlin, 1992.
12. V. Gafiychuk, B. Datsko, and V. Meleshko, Mathematical modeling of time fractional reaction-diffusion systems, J. Comput. Appl. Math. 220 (2008), no. 1-2, 215-225.
13. J. Henderson and A. Ouahab, Fractional functional differential inclusions with finite delay, Nonlinear Anal. 70 (2009), no. 5, 2091-2105.
14. S. Hu and N. Papageorgiou, Handbook of Multivalued Analysis. Vol. I, Kluwer Academic Publishers, Dordrecht, 1997.
15. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
16. S. Ladaci, J. L. Loiseau, and A. Charef, Fractional order adaptive high-gain controllers for a class of linear systems, Commun. Nonlinear Sci. Numer. Simul. 13 (2008), no. 4, 707-714.
17. A. Lasota and Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781-786.
18. M. P. Lazarević, Finite time stability analysis of PD∞ fractional control of robotic timedelay systems, Mech. Res. Comm. 33 (2006), no. 2, 269-279.
19. W. S. Li, Y. K. Chang, and J. J. Nieto, Solvability of impulsive neutral evolution differential inclusions with state-dependent delay, Math. Comput. Modelling 49 (2009), no. 9-10, 1920-1927.
20. J. J. Nieto and R. Rodŕi{dotless}guez-Ĺopez, Euler polygonal method for metric dynamical systems, Inform. Sci. 177 (2007), no. 20, 4256-4270.
21. A. Ouahab, Some results for fractional boundary value problem of differential inclusions, Nonlinear Anal. 69 (2008), no. 11, 3877-3896.
22. I. Podlubny, Fractional Differential Equations, Academic Press, Inc., San Diego, CA, 1999.
23. S. Z. Rida, H. M. El-Sherbiny, and A. A. M. Arafa, On the solution of the fractional nonlinear Schrodinger equation, Phys. Lett. A 372 (2008), no. 5, 553-558.
24. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon, 1993.
25. G. V. Smirnov, Introduction to the Theory of Differential Inclusions, Graduate Studies in Mathematics, 41. American Mathematical Society, Providence, RI, 2002.
26. S. Zhang, Existence of solution for a boundary value problem of fractional order, Acta Math. Sci. Ser. B Engl. Ed. 26 (2006), no. 2, 220-228.