Unbounded solutions to a boundary value problem of fractional order on the half-line

Computers and Mathematics with Applications

Volumn 61, Issue 4, 2011, Pages 1079-1087

  Su, Xinwei ^a   Zhang, Shuqin ^a  

^a CHINA UNIVERSITY OF MINING AND TECHNOLOGY   (China)

Author keywords

Boundary value problem; Fixed point theorem; Fractional differential equation; Infinite interval; Unbounded solution

Indexed keywords

COMPACTNESS CRITERION; EXISTENCE RESULTS; FIXED POINT THEOREM; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIAL EQUATION; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL ORDER; HALF-LINE; INFINITE INTERVAL; NONLINEAR TERMS; SCHAUDER'S FIXED POINT THEOREM; SEMI-INFINITE INTERVALS; UNBOUNDED DOMAIN; UNBOUNDED SOLUTION;

BANACH SPACES; NONLINEAR EQUATIONS;

BOUNDARY VALUE PROBLEMS;

EID: 79651475787     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.12.058     Document Type: Article

References (24)

1. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations 2006 Elsevier B. V. Amsterdam
2. I. Podlubny Fractional Differential Equations Mathematics in Science and Engineering vol. 198 1999 Academic Press New York, London, Toronto
3. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional Integrals and Derivatives: Theory and Applications 1993 Gordon and Breach Yverdon
4. R.P. Agarwal, V. Lakshmikantham, and J.J. Nieto On the concept of solution for fractional differential equations with uncertainty Nonlinear Anal. 72 2010 2859 2862
5. D. Araya, and C. Lizama Almost automorphic mild solutions to fractional differential equations Nonlinear Anal. 69 2008 3692 3705
6. M. Benchohra, J. Henderson, S.K. Ntouyas, and A. Ouahab Existence results for fractional order functional differential equations with infinite delay J. Math. Anal. Appl. 338 2008 1340 1350
7. S.D. Eidelman, and A.N. Kochubei Cauchy problem for fractional diffusion equations J. Differential Equations 199 2004 211 255
8. M.M. El-Borai Semigroups and some nonlinear fractional differential equations Appl. Math. Comput. 149 2004 823 831
9. O.K. Jaradat, A. Al-Omari, and S. Momani Existence of the mild solution for fractional semilinear initial value problems Nonlinear Anal. 69 2008 3153 3159
10. V. Lakshmikantham Theory of fractional functional differential equations Nonlinear Anal. 69 2008 3337 3343
11. V. Lakshmikantham, and A.S. Vatsala General uniqueness and monotone iterative technique for fractional differential equations Appl. Math. Lett. 21 2008 828 834
12. S. Zhang Monotone iterative method for initial value problem involving RiemannLiouville fractional derivatives Nonlinear Anal. 71 2009 2087 2093
13. Y. Zhou Existence and uniqueness of fractional functional differential equations with unbounded delay Int. J. Dyn. Syst. Differ. Equ. 1 2008 239 244
14. B. Ahmad Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations Appl. Math. Lett. 23 2010 390 394
15. Z.B. Bai, and H.S. Lü Positive solutions for boundary value problem of nonlinear fractional differential equation J. Math. Anal. Appl. 311 2005 495 505
16. M. Benchohra, S. Hamani, and S.K. Ntouyas Boundary value problems for differential equations with fractional order and nonlocal conditions Nonlinear Anal. 71 2009 2391 2396
17. V.D. Gejji, and S. Bhalekar Boundary value problems for multi-term fractional differential equations J. Math. Anal. Appl. 345 2008 754 765
18. H. Jafari, and V.D. Gejji Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method Appl. Math. Comput. 180 2006 700 706
19. H.A.H. Salem On the fractional m-point boundary value problem in reflexive Banach space and the weak topologies J. Comput. Appl. Math. 224 2009 565 572
20. X. Su Boundary value problem for a coupled system of nonlinear fractional differential equations Appl. Math. Lett. 22 2009 64 69
21. 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 1838 1843
22. X. Su, and S. Zhang Solutions to boundary-value problems for nonlinear differential equations of fractional order Electron. J. Differential Equations 2009 26 2009 1 15
23. A. Arara, M. Benchohra, N. Hamidi, and J.J. Nieto Fractional order differential equations on an unbounded domain Nonlinear Anal. 72 2010 580 586
24. X.K. Zhao, and W.G. Ge Unbounded solutions for a fractional boundary value problem on the infinite interval Acta Appl. Math. 109 2010 495 505