Existence results for a coupled system of nonlinear fractional 2m-point boundary value problems at resonance

Advances in Difference Equations

Volumn 2011, Issue , 2011, Pages

  Wang, Gang ^a   Liu, Wenbin ^a   Zhu, Sinian ^a   Zheng, Ting ^a  

^a CHINA UNIVERSITY OF MINING AND TECHNOLOGY   (China)

Author keywords

2m point boundary conditions; Coincidence degree; Fractional nonlinear differential equation

Indexed keywords

EID: 84868114263     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/1687-1847-2011-44     Document Type: Article

References (16)

1. Kilbas, AA, Srivastava, HM, Trujillo, JJ: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies. pp. 204. Elsevier Science B.V., Amsterdam (2006)
2. Sabatier, J, Agrawal, OP, Machado, JAT, eds: Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007)
3. Lakshmikantham, V, Leela, S, Vasundhara Devi, J: Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge (2009)
4. Samko, SG, Kilbas, AA, Marichev, OI: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, New York (1993)
5. Lakshmikantham, V, Vatsala, AS: Basic theory of fractional differential equations. Nonlinear Anal Theory Methods Appl. 69, 2677-2682 (2008). doi:10.1016/j.na.2007.08.042
6. Lakshmikantham, V: Theory of fractional functional differential equations. Nonlinear Anal Theory Methods Appl. 69, 3337-3343 (2008). doi:10.1016/j.na.2007.09.025
7. Lakshmikantham, V, Vatsala, AS: General uniqueness and monotone iterative technique for fractional differential equations. Appl Math Lett. 21, 828-834 (2008). doi:10.1016/j.aml.2007.09.006
8. El-Sayed, AMA, El-Mesiry, AEM, El-Saka, HAA: On the fractional-order logistic equation. Appl Math Lett. 20, 817-823 (2007). doi:10.1016/j.aml.2006. 08.013
9. El-Sayed, AMA, El-Maghrabi, EM: Stability of a monotonic solution of a non-autonomous multidimensional delay differential equation of arbitrary (fractional) order. Electron J Qualitative Theory Differential Equations. 16, 1-9 (2008)
10. Diethelm, K, Ford, NJ: Analysis of fractional differential equations. J Math Anal Appl. 265, 229-248 (2002). doi:10.1006/ jmaa.2000.7194
11. Bai, C: Positive solutions for nonlinear fractional differential equations with coefficient that changes sign. Nonlinear Anal Theory Methods Appl. 64, 677-685 (2006). doi:10.1016/j.na.2005.04.047
12. Su, X: Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl Math Lett. 22, 64-69 (2009). doi:10.1016/j.aml.2008.03.001
13. Zhang, Y, Bai, Z: Existence of positive solutions for s nonlinear fractional three-point boundary value problen at resonance. Appl Math Comput
14. Bai, Z: On solutions of some fractional m-point boundary value problems at resonance. Electron J Qualitative Theory Differential Equations. 37, 1-15 (2010)
15. Mawhin, J: Topological degree and boundary value problems for nonlinear differential equations. In: Fitzpatrick PM, Martelli M, Mawhin J, Nussbaum R (eds.) Topological Methods for Ordinary Differential Equations. Lecture Notes in Mathematics, vol. 1537, pp. 74-142. Springer, Berlin (1991)
16. Hu, Z, Liu, W: Solvability for fractional order boundary value problem at resonance. Bound Value Problem. 20, 1-10 (2011)