Existence results for boundary value problems of nonlinear fractional differential equations

Computers and Mathematics with Applications

Volumn 62, Issue 5, 2011, Pages 2374-2382

  Chai, Guoqing ^a  

^a HUBEI NORMAL UNIVERSITY   (China)

Author keywords

Boundary value problem; Existence of solution; Fixed point theorem; Fractional differential equations

Indexed keywords

BOUNDARY VALUES; CAPUTO DERIVATIVES; CONTRACTION MAPPING PRINCIPLES; EXISTENCE OF SOLUTIONS; EXISTENCE RESULTS; FIXED POINT THEOREMS; FRACTIONAL DIFFERENTIAL EQUATIONS; SCHAUDER FIXED-POINT THEOREM;

BANACH SPACES; BOUNDARY VALUE PROBLEMS;

NONLINEAR EQUATIONS;

EID: 80052268620     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.07.025     Document Type: Article

References (22)

1. W.G. Glockle, and T.F. Nonnenmacher A fractional calculus approach of self-similar protein dynamics Biophys. J. 68 1995 46 53
2. R. Hilfer Applications of Fractional Calculus in Physics 2000 World Scientific Singapore
3. F. Metzler, W. Schick, H.G. Kilian, and T.F. Nonnenmacher Relaxation in filled polymers: a fractional calculus approach J. Chem. Phys. 103 1995 7180 7186
4. I. Podlubny Fractional Differential Equations 1999 Academic Press San Diego
5. I. Podlubny Geometric and physical interpretation of fractional integration and fractional differentiation Fract. Calc. Appl. Anal. 5 2002 367 386
6. A.A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo North-Holland Mathematics Studies Theory and Applications of Fractional Differential Equations vol. 204 2006 Elsevier Science B.V, Amsterdam
7. V. Lakshmikantham, S. Leela, and J. Vasundhara Theory of Fractional Dynamic Systems 2009 Cambridge Academic Publishers Cambridge
8. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional Integrals and Derivaes Theory and Applications 1993 Gordon and Breach Science Publisher
9. 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
10. V. Lakshmikanthama, and A.S. Vatsala General uniqueness and monotone iterative technique for fractional differential equations Appl. Math. Lett. 21 2008 828 834
11. V. Lakshmikanthama Theory of fractional functional differential equations Nonlinear Anal. 69 2008 3337 3343
12. Ravi P. Agarwal, Donal O'Regan, and Svatoslav Stanek Positive solutions for Dirichlet problems of singular nonlinear fractional, differential equations J. Math. Anal. Appl. 371 2010 57 68
13. F.A. McRae Monotone iterative technique and existence results for fractional differential equtions Nonlinear Anal. 71 2009 6093 6096
14. M. Benchohra, S. Hamani, and S.K. Ntouyas Boundary value problems for differential equational with fractional order and nonlocal condtions Nonlinear Anal. 71 2009 2391 2396
15. R.P. Agarwal, Yong Zhou, and Yunyun He Existence of fractional neutral functional differential equations Comput. Math. Appl. 59 2010 1095 1100
16. Bashir Ahmad, and Juan 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
17. Shuqin Zhang, Positive solutions for boundary-value problems of nonlinear fractional differential equations, Electron. J. Differential Equations, 2006, (36), 112.
18. Mujeeb ur Rehman, and Rahmat Ali Khan Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations Appl. Math. Lett. 2010 1038 1044
19. Krishnan Balachandran, and Juan J. Trujillo The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces Nonlinear Anal. 72 2010 4587 4593
20. 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 2 2008 1340 1350
21. Dumitru Baleanu, and Octavian G. Mustafa On the global existence of solutions to a class of fractional differential equations Comput. Math. Appl. 59 2010 1835 1841
22. Moustafa El-Shahed Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order Comput. Math. Appl. 59 2010 3438 3443