On solutions of some fractional m-point boundary value problems at resonance

Electronic Journal of Qualitative Theory of Differential Equations

Volumn , Issue , 2010, Pages 1-15

  Bai, Zhanbing ^a  

^a SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

At resonance; Coincidence degree; Fractional differential equation; m point boundary value problem

Indexed keywords

EID: 77955203208     PISSN: None     EISSN: 14173875     Source Type: Journal    
DOI: 10.14232/ejqtde.2010.1.37     Document Type: Article

References (25)

1. R.P. Agarwal, M. Belmekki, and M. Benchohra, A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative. Adv. Difference Equ. 2009, Art. ID 981728, 47 pages.
2. R.P. Agarwal, M. Benchohra and S. Hamani, A survey on existence result for boundary value problems of nonlinear fractional differential equations and inclusions, Acta. Appl. Math. 109 (2010) 973-1033.
3. B. Ahmad, J.J. Nieto, Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations. Abstract Appl. Anal. Volume 2009 (2009), Article ID 494720, 9 pages.
4. A. Babakhani, V.D. Gejji, Existence of positive solutions of nonlinear fractional differential equations, J. Math. Anal. Appl. 278 (2003) 434-442.
5. Z.B. Bai and H.S. Lü, Positive solutions of boundary value problems of nonlinear fractional differential equation, J. Math. Anal. Appl. 311 (2005) 495-505.
6. Z.B. Bai, On positive solutions of nonlocal fractional boundary value problem, Nonlinear Anal. 72(2009) 916-924.
7. Z.B. Bai, On solutions of nonlinear fractional m-point boundary value problem at resonance (I), submitted.
8. Z.B. Bai and T.T. Qiu, Existence of positive solution for singular fractional differential equation, Appl. Math. Comp. 215 (2009) 2761-2767.
9. M. Belmekki, J.J. Nieto, R. Rodriguez-Lopez, Existence of periodic solutions for a nonlinear fractional differential equation. Boundary Value Problems 2009 (2009), Art. ID. 324561.
10. D. Delbosco, Existence and Uniqueness for a Nonlinear Fractional Differential Equation, J. Math. Anal. Appl. 204 (1996) 609-625.
11. A.M.A. El-Sayed, Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal. 33 (1998) 181-186.
12. W. Feng, J.R.L. Webb, Solvability of m-point boundary value problems with non-linear growth, J. Math. Anal. Appl. 212 (1997) 467-480.
13. C.P. Gupta, A second order m-point boundary value problem at resonance, Nonlinear Anal. TMA 24 (1995) 1483-1489.
14. V.A. Il'in, E.I. Moiseev, Nonlocal boundary value problems of the second kind for a Sturm-Liouville operator, Diff. Equa. 23 (1987) 979-987.
15. J. Henderson and A. Ouahab, Fractional functional differential inclusions with finite delay, Nonlinear Anal. TMA 70 (2009) 2091-2105.
16. S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives (Theory and Applications), Gordon and Breach, Switzerland, 1993.
17. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier B.V., Netherlands, 2006.
18. V. Lakshmikantham, A.S. Vatsala, Basic theory of fractional differential equations, Nonlinear Anal. TMA 69 (8) (2008) 2677-2682.
19. V. Lakshmikantham, S. Leela, J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.
20. V. Lakshmikantham, S. Leela, A Krasnosel'skii-Krein-type uniqueness result for fractional differential equations, Nonlinear Anal. TMA 71 (2009) 3421-3424.
21. B. Liu, Solvability of multi-point boundary value problem at resonance (II), Appl. Math. Comput. 136 (2003) 353-377.
22. J. Mawhin, Topological degree methods in nonlinear boundary value problems, in: NSFCBMS Regional Conference Series in Mathematics, American Mathematical Society, Providence, RI, 1979.
23. K.S. Miller, Fractional differential equations, J. Fract. Calc. 3 (1993) 49-57.
24. I. Podlubny, Fractional Differential Equation, Academic Press, San Diego, 1999.
25. Y. Zhou, Existence and uniqueness of fractional functional differential equations with unbounded delay, Int. J. Dyn. Syst. Differ. Equ. 1 (4) (2008), 239-244.