Existence of solutions for multi-point nonlinear differential equations of fractional orders with integral boundary conditions

Electronic Journal of Differential Equations

Volumn 2012, Issue , 2012, Pages 1-10

  Wang, Gang ^a   Liu, Wenbin ^a   Ren, Can ^a  

^a CHINA UNIVERSITY OF MINING AND TECHNOLOGY   (China)

Author keywords

Boundary value problem; Existence and uniqueness; Fixed point theorem; Fractional differential equation

Indexed keywords

EID: 84860877187     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. B. Ahmad, J. J. Nieto; Anti-periodic fractional boundary value problems, Comput. Math. Appl.doi:10.1016/j.camwa.2011.02.034.
2. B. Ahmad, V. Otero-Espinar; Existence of solutions for fractional differential inclusions with anti-periodic boundary conditions, Bound. Value Probl.(2009) Art. ID 625347, 11 pp.
3. B. Ahmad, 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.
4. B. Ahmad; Existence of solutions for fractional differential equations of order q ∈ (2, 3] with anti-periodic boundary conditions, J. Appl.Math. Comput. 34 (2010) 385-391.
5. B. Ahmad, J. J. Nieto; Existence of solutions for anti-periodic boundary value problems involving fractional differential equations via Leray-Schauder degree theory, Topol. Methods Nonlinear Anal. 35 (2010) 295-304.
6. B. Ahmad, A. Alsaedi, B. S. Alghamdi; Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions, Nonlinear Analysis, 9 (2008) 1727-1740.
7. B. Ahmad, A. Alsaedi; Existence of approximate solutions of the forced Duffing equation with discontinuous type integral boundary conditions, Nonlinear Analysis, 10 (2009) 358-367.
8. C. Bai; Positive solutions for nonlinear fractional differential equations with coefficient that changes sign Nonlinear Analysis: Theory, Methods and Applications, 64 (2006) 677-685.
9. A. Boucherif; Second-order boundary value problems with integral boundary conditions, Nonlinear Analysis, 70 (2009) 364-371.
10. Y. K. Chang, J. J. Nieto, W.S. Li; On impulsive hyperbolic differential inclusions with nonlocal initial conditions, Journal of Optimization Theory and Applications, 140 (2009) 431-442.
11. K. Diethelm, N. J. Ford; Analysis of fractional differential equations, Journal of Mathematical Analysis and Applications,265 (2002) 229-248.
12. Z. Hu, W. Liu; Solvability for fractional order boundary value problem at resonance, Boundary value problem, 20 (2011) 1-10.
13. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo; Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
14. V. Lakshmikantham, S. Leela, J. Vasundhara Devi; Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.
15. V. Lakshmikantham A. S. Vatsala; General uniqueness and monotone iterative technique for fractional differential equations, Applied Mathematics Letters, 21 (2008) 828-834.
16. J. Sabatier, O. P. Agrawal, J. A. T. Machado (Eds.); Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, 2007.
17. S. G. Samko, A. A. Kilbas, O. I. Marichev; Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, New York, NY, USA, 1993.
18. D. R. Smart; Fixed Point Theorems, Cambridge University Press, 1980.
19. X. Su; Boundary value problem for a coupled system of nonlinear fractional differential equations, Applied Mathematics Letters, 22 (2009) 64-69.
20. G. Wang, W. Liu; The existence of solutions for a fractional 2m-point boundary value problems, Journal of Applied Mathematics. (in press)
21. G. Wang, W. Liu; Existence results for a coupled system of nonlinear fractional 2m-point boundary value problems at resonance, Advances in difference equations, doi:10.1186/1687-1847-2011-44.
22. G. Wang, B. Ahmad, L. Zhang; Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order, Nonlinear Anal. Theory, Methods Appl. 74 (3) (2011) 792-804.