Existence results for a coupled system of nonlinear fractional three-point boundary value problems at resonance

Computers and Mathematics with Applications

Volumn 61, Issue 4, 2011, Pages 1032-1047

  Zhang, Yinghan ^a   Bai, Zhanbing ^a   Feng, Tingting ^a  

^a SHANDONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

At resonance; Coincidence degree; Coupled system; Fractional differential equations

Indexed keywords

AT RESONANCE; COINCIDENCE DEGREE; COINCIDENCE DEGREE THEORY; COUPLED SYSTEMS; EXISTENCE RESULTS; FRACTIONAL DIFFERENTIAL EQUATIONS; THREE POINT BOUNDARY VALUE PROBLEMS;

BANACH SPACES; BOUNDARY CONDITIONS; RESONANCE; TOPOLOGY;

NONLINEAR EQUATIONS;

EID: 79651475091     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.12.053     Document Type: Article

References (29)

1. R.P. Agarwal, V. Lakshmikantham, and J.J. Nieto On the concept of solution for fractional differential equations with uncertainty Nonlinear Anal. TMA 72 2010 2859 2862
2. 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
3. A. Babakhani, and V.D. Gejji Existence of positive solutions of nonlinear fractional differential equations J. Math. Anal. Appl. 278 2003 434 442
4. Z. Bai On positive solutions of a nonlocal fractional boundary value problem Nonlinear Anal. TMA 72 2010 916 924
5. Z. Bai, and H. Lü Positive solutions of boundary value problems of nonlinear fractional differential equation J. Math. Anal. Appl. 311 2005 495 505 (Pubitemid 41350217)
6. Z. Bai, and Y. Zhang The existence of solutions for a fractional multi-point boundary value problem Comput. Math. Appl. 60 2010 2364 2372
7. D. Baleanu, and O.G. Mustafa On the global existence of solutions to a class of fractional differential equations Comput. Math. Appl. 59 2010 1835 1841
8. D. Baleanu, and O.G. Mustafa On the asymptotic integration of a class of sublinear fractional differential equations J. Math. Phys. 50 2009 123520 10.1063/1.3271111 (14 pages)
9. D. Baleanu, O.G. Mustafa, and R.P. Agarwal On the solution set for a class of sequential fractional differential equations J. Phys. A: Math. Theor. 43 2010 385209 10.1088/1751-8113/43/38/385209
10. B. Bonilla, M. Rivero, L. Rodriguez-Germa, and J.J. Trujillo Fractional differential equations as alternative models to nonlinear differential equations Appl. Math. Comput. 187 2007 79 88 (Pubitemid 46635706)
11. Y.K. Chang, and J.J. Nieto Some new existence results for fractional differential inclusions with boundary conditions Math. Comput. Modelling 49 2009 605 609
12. Y. Chen, and H. An Numerical solutions of coupled Burgers equations with time and space fractional derivatives Appl. Math. Comput. 200 2008 87 95
13. A.M.A. El-Sayed Nonlinear functional differential equations of arbitrary orders Nonlinear Anal. TMA 33 1998 181 186
14. V. Gafiychuk, B. Datsko, and V. Meleshko Mathematical modeling of time fractional reactiondiffusion systems J. Comput. Appl. Math. 220 2008 215 225
15. V.D. Gejji Positive solutions of a system of non-autonomous fractional differential equations J. Math. Anal. Appl. 302 2005 56 64
16. A.A. Kilbas, O.I. Marichev, and S.G. Samko Fractional Integral and Derivatives (Theory and Applications) 1993 Gordon and Breach Switzerland
17. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations 2006 Elsevier B.V. Netherlands
18. V. Lakshmikantham, S. Leela, and J. Vasundhara Devi Theory of Fractional Dynamic Systems 2009 Cambridge Academic Publishers Cambridge
19. V. Lakshmikantham, and A.S. Vatsala Basic theory of fractional differential equations Nonlinear Anal. TMA 69 2008 2677 2682
20. V. Lakshmikantham, and S. Leela Nagumo-type uniqueness result for fractional differential equations Nonlinear Anal. TMA 71 2009 2886 2889
21. V. Lakshmikantham, and S. Leela A KrasnoselskiiKrein-type uniqueness result for fractional differential equations Nonlinear Anal. TMA 71 2009 3421 3424
22. V. Lakshmikantham, and A.S. Vatsala Theory of fractional differential inequalities and applications Commun. Appl. Anal. 11 2007 395 402
23. V. Lakshmikantham, and A.S. Vatsala General uniqueness and monotone iterative technique for fractional differential equations Appl. Math. Lett. 21 2008 828 834
24. M.P. Lazarevi Finite time stability analysis of P Dα fractional control of robotic time-delay systems Mech. Res. Comm. 33 2006 269 279
25. K.S. Miller Fractional differential equations J. Fract. Calc. 3 1993 49 57
26. X. Su Boundary value problem for a coupled system of nonlinear fractional differential equations Appl. Math. Lett. 22 2009 64 69
27. Y. Zhang, and Z. Bai Existence of solutions for nonlinear fractional three-point boundary value problems at resonance J. Appl. Math. Comput. 2010 10.1007/s12190-010-0411-x
28. B. Liu Solvability of multi-point boundary value problem at resonance II Appl. Math. Comput. 136 2003 353 377
29. J. Mawhin Topological degree and boundary value problems for nonlinear differential equations P.M. Fitzpatrick, M. Martelli, J. Mawhin, R. Nussbaum, Topological Methods for Ordinary Differential Equatons Lecture Notes in Mathematics vol. 1537 1991 Springer Berlin 74 142