Han, Xiaoling; Wang, Ting The existence of solutions for a nonlinear fractional multi-point boundary value problem at resonance. (English) Zbl 1242.34007 Int. J. Differ. Equ. 2011, Article ID 401803, 14 p. (2011). Summary: We discuss the existence of solutions for a multipoint boundary value problem of fractional differential equation. An existence result is obtained with the use of the coincidence degree theory. Cited in 5 Documents MSC: 34A08 Fractional ordinary differential equations 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:coincidence degree theory PDF BibTeX XML Cite \textit{X. Han} and \textit{T. Wang}, Int. J. Differ. Equ. 2011, Article ID 401803, 14 p. (2011; Zbl 1242.34007) Full Text: DOI References: [1] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2006. · Zbl 1206.26007 [2] K. S. Miller, “Fractional differential equations,” Journal of Fractional Calculus, vol. 3, pp. 49-57, 1993. · Zbl 0789.26002 [3] Z. Bai and H. Lü, “Positive solutions for boundary value problem of nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 311, no. 2, pp. 495-505, 2005. · Zbl 1079.34048 [4] A. Babakhani and V. Daftardar-Gejji, “Existence of positive solutions of nonlinear fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 278, no. 2, pp. 434-442, 2003. · Zbl 1027.34003 [5] V. Daftardar-Gejji and A. Babakhani, “Analysis of a system of fractional differential equations,” Journal of Mathematical Analysis and Applications, vol. 293, no. 2, pp. 511-522, 2004. · Zbl 1058.34002 [6] F. Meng and Z. Du, “Solvability of a second-order multi-point boundary value problem at resonance,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 23-30, 2009. · Zbl 1168.34310 [7] Y. H. Zhang and Z. B. Bai, “Exitence of solutions for nonlinear fractional three-point boundary value problem at resonance,” Journal of Applied Mathematics and Computing, vol. 36, no. 1-2, pp. 417-440, 2011. · Zbl 1225.34013 [8] H. Jafari and V. Daftardar-Gejji, “Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method,” Applied Mathematics and Computation, vol. 180, no. 2, pp. 700-706, 2006. · Zbl 1102.65136 [9] C. Yu and G. Z. Gao, “On the solution of nonlinear fractional order differential equation,” Nonlinear Analysis, vol. 63, no. 5-7, pp. e971-e976, 1998. · Zbl 1224.34005 [10] N. Kosmatov, “A multi-point boundary value problem with two critical conditions,” Nonlinear Analysis, vol. 65, no. 3, pp. 622-633, 2006. · Zbl 1121.34023 [11] B. Liu and Z. Zhao, “A note on multi-point boundary value problems,” Nonlinear Analysis, vol. 67, no. 9, pp. 2680-2689, 2007. · Zbl 1127.34006 [12] R. P. Agarwal, V. Lakshmikantham, and J. J. Nieto, “On the concept of solution for fractional differential equations with uncertainty,” Nonlinear Analysis, vol. 72, no. 6, pp. 2859-2862, 2010. · Zbl 1188.34005 [13] Y.-K. Chang and J. J. Nieto, “Some new existence results for fractional differential inclusions with boundary conditions,” Mathematical and Computer Modelling, vol. 49, no. 3-4, pp. 605-609, 2009. · Zbl 1165.34313 [14] A. M. A. El-Sayed, “Nonlinear functional-differential equations of arbitrary orders,” Nonlinear Analysis, vol. 33, no. 2, pp. 181-186, 1998. · Zbl 0934.34055 [15] D. Guo and J. Sun, Nonlinear Integral Equations, Shandong Science and Technology Press, Jinan, China, 1987. [16] V. Lakshmikantham and S. Leela, “Nagumo-type uniqueness result for fractional differential equations,” Nonlinear Analysis, vol. 71, no. 7-8, pp. 2886-2889, 2009. · Zbl 1177.34003 [17] V. Lakshmikantham and S. Leela, “A Krasnoselskii-Krein-type uniqueness result for fractional differential equations,” Nonlinear Analysis, vol. 71, no. 7-8, pp. 3421-3424, 2009. · Zbl 1177.34004 [18] J. Mawhin, “Topological degree and boundary value problems for nonlinear differential equations,” in Topological Methods for Ordinary Differential Equations, P. M. Fitzpatrick, M. Martelli, J. Mawhin, and R. Nussbaum, Eds., vol. 1537 of Lecture Notes in Mathematics, pp. 74-142, Springer, Berlin, Germany, 1991. · Zbl 0798.34025 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.