The eigenvalue problem for a singular higher order fractional differential equation involving fractional derivatives

Applied Mathematics and Computation

Volumn 218, Issue 17, 2012, Pages 8526-8536

  Zhang, Xinguang ^a   Liu, Lishan ^b,c   Wu, Yonghong ^c  

^a YANTAI UNIVERSITY   (China)

^b QUFU NORMAL UNIVERSITY   (China)

^c CURTIN UNIVERSITY   (Australia)

Author keywords

Eigenvalue problem; Fractional differential equation; Green function; Positive solution

Indexed keywords

EIGENVALUE PROBLEM; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATIONS; SCHAUDER'S FIXED POINT THEOREM; SINGULAR EIGENVALUE PROBLEMS; UPPER AND LOWER SOLUTIONS METHOD;

DIFFERENTIAL EQUATIONS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 84862776655     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.02.014     Document Type: Article

References (22)

1. Z. Bai On positive solutions of a nonlocal fractional boundary value problem Nonlinear Anal. 72 2010 916 924
2. S. Zhang Positive solutions to singular boundary value problem for nonlinear fractional differential equation Comput. Math. Appl. 59 2010 1300 1309
3. C.S. Goodrich Existence of a positive solution to a class of fractional differential equations Appl. Math. Lett. 23 2010 1050 1055
4. C.S. Goodrich Existence of a positive solution to systems of differential equations of fractional order Comput. Math. Appl. 62 2011 1251 1268
5. Y. Wang, L. Liu, and Y. Wu Positive solutions for a nonlocal fractional differential equation Nonlinear Anal. 74 2011 3599 3605
6. B. Ahmad, and A. Alsaedi Existence and uniqueness of solutions for coupled systems of higher-order nonlinear fractional differential equations Fixed Point Theory Appl. 2010 2010 (Article ID 364560, 17 pages)
7. B. Ahmad, and J. Nieto Existence of solutions for nonlocal boundary value problems of higher-order nonlinear fractional differential equations Abstr. Appl. Anal. 2009 2009 (Article ID 494720, 9 pages)
8. K. Miller, and B. Ross An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 Wiley New York
9. I. Podlubny Fractional Differential Equations Mathematics in Science and Engineering 1999 Academic Press New York, London, Toronto
10. A. Kilbas, H. Srivastava, and J. Trujillo Theory and Applications of Fractional Differential Equations 2006 Elsevier B.V. Netherlands
11. M. Feng, X. Zhang, and W. Ge New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions Bound. Value Probl. 2011 2011 (Article ID 720702, 20 pages)
12. M. El-Shahed, and J. Nieto Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order Comput. Math. Appl. 59 2010 3438 3443
13. B. Ahmad, and J. Nieto Existence results for higher order fractional differential inclusions with nonlocal boundary conditions Nonlinear Stud. 17 2010 131 138
14. A. Hussein Salem On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies J. Comput. Appl. Math. 224 2009 565 572
15. M. Rehman, and R. Khan Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations Appl. Math. Lett. 23 2010 1038 1044
16. V. Lakshmikantham, and A. Vatsala General uniqueness and monotone iterative technique for fractional differential equations Appl. Math. Lett. 21 2008 828 834
17. T. Bhaskar, V. Lakshmikantham, and S. Leela Fractional differential equations with a Krasnoselskii-Krein type condition Nonlinear Anal. 3 2009 734 737
18. Z. Bai, and H. Lü Positive solutions for boundary value problem of nonlinear fractional differential equation J. Math. Anal. Appl. 311 2005 495 505
19. X. Zhang, and Y. Han Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations Appl. Math. Lett. 25 2012 555 560
20. B. Ahmad, and A. Alsaedi Existence of solutions for anti-periodic boundary value problems of nonlinear impulsive functional integro-differential equations of mixed type Nonlinear Anal. Hybrid Syst. 3 2009 501 509
21. M. Benchohraa, S. Hamania, and S. Ntouyas Boundary value problems for differential equations with fractional order and nonlocal conditions Nonlinear Anal. 71 2009 2391 2396
22. X. Zhang, L. Liu, and Y. Wu Multiple positive solutions of a singular fractional differential equation with negatively perturbed term Math. Comput. Modelling 55 2012 1263 1274