×

Existence results for the three-point impulsive boundary value problem involving fractional differential equations. (English) Zbl 1193.34007

Summary: We consider the existence of solutions for a class of three-point boundary value problems involving nonlinear impulsive fractional differential equations. By use of Banach’s fixed point theorem and Schauder’s fixed point theorem, some existence results are obtained.

MSC:

34A08 Fractional ordinary differential equations
26A33 Fractional derivatives and integrals
34B37 Boundary value problems with impulses for ordinary differential equations
45J05 Integro-ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Babakhani, A.; Gejji, V. D., Existence of positive solutions of nonlinear fractional differential equations, J. Math. Anal. Appl., 278, 434-442 (2003) · Zbl 1027.34003
[2] Bai, C.; Fang, J., The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations, Appl. Math. Comput., 150, 611-621 (2004) · Zbl 1061.34001
[3] Bai, Z.; Lü, H., Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Math. Anal. Appl., 311, 495-505 (2005) · Zbl 1079.34048
[4] Chang, Y.; Nieto, J., Some new existence results for fractional differential inclusions with boundary conditions, Math. Comput. Modelling, 49, 605-609 (2009) · Zbl 1165.34313
[5] Delbosco, D., Fractional calculus and function spaces, J. Fract. Calc., 6, 45-53 (1994) · Zbl 0829.46018
[6] Jafari, H.; Gejji, V. D., Positive solutions of nonlinear fractional boundary value problems using a domain decomposition method, Appl. Math. Comput., 180, 700-706 (2006) · Zbl 1102.65136
[7] Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., (Theory and Applications of Fractional Differential Equations. Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204 (2006), Elsevier Science B.V.: Elsevier Science B.V. Amsterdam) · Zbl 1092.45003
[8] Salem, H. A.H., On the fractional order \(m\)-point boundary value problem in reflexive Banach spaces and weak topologies, J. Comput. Appl. Math., 224, 567-572 (2009) · Zbl 1176.34070
[9] Zhang, S., Positive solutions for boundary value problem of nonlinear fractional differential equations, Electron. J. Differential Equations, 2006, 1-12 (2006)
[10] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), Worlds Scientific: Worlds Scientific Singapore · Zbl 0719.34002
[11] Samoilenko, A. M.; Perestyuk, N. A., Impulsive Differential Equations (1995), World Scientific: World Scientific Singapore · Zbl 0837.34003
[12] Lee, E. K.; Lee, Y. H., Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equation, Appl. Math. Comput., 158, 745-759 (2004) · Zbl 1069.34035
[13] Lin, X.; Jiang, D., Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations, J. Math. Anal. Appl., 321, 501-514 (2006) · Zbl 1103.34015
[14] Nieto, J. J.; Lópe, R. R., Boundary value problems for a class of impulsive functional equations, Comput. Math. Appl., 55, 2715-2731 (2008) · Zbl 1142.34362
[15] Shen, J.; Wang, W., Impulsive boundary value problems with nonlinear boundary conditions, Nonlinear Anal., 69, 4055-4062 (2008) · Zbl 1171.34309
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.