Positive solutions to singular boundary value problem for nonlinear fractional differential equation. (English) Zbl 1189.34050

Summary: We consider the existence of positive solutions to the singular boundary value problem for fractional differential equation. Our analysis relies on a fixed point theorem for the mixed monotone operator.


34B15 Nonlinear boundary value problems for ordinary differential equations
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
45J05 Integro-ordinary differential equations
Full Text: DOI


[1] Kilbas, A.A.; Srivastava, H.M.; Trujillo, J.J., Theory and applications of fractional differential equations, (2006), Elsevier Amsterdam · Zbl 1092.45003
[2] Ouahab, Abdelghani, Some results for fractional boundary value problem of differential inclusions, Nonlinear analysis, 69, 11, 3877-3896, (2008) · Zbl 1169.34006
[3] Salem, Hussein A.H., On the fractional order \(m\)-point boundary value problem in reflexive Banach spaces and weak topologies, Journal of computational and applied mathematics, 224, 2, 565-572, (2009) · Zbl 1176.34070
[4] Benchohra, M.; Hamania, S.; Ntouyas, S.K., Boundary value problems for differential equations with fractional order and nonlocal conditions, Nonlinear analysis, 71, 7-8, 2564-2575, (2009)
[5] Su, Xinwei, Boundary value problem for a coupled system of nonlinear fractional differential equations, Applied mathematics letters, 22, 1, 64-69, (2009) · Zbl 1163.34321
[6] Xiaojie Xu, Daqing Jiang, Chengjun Yuan, Multiple positive solutions for boundary value problem of nonlinear fractional differential equation, Nonlinear Analysis (in press) · Zbl 1178.34006
[7] Zhang, Shuqin, Existence results of positive solutions to boundary value problem for fractional differential equation, Positivity, 13, 583-599, (2009) · Zbl 1202.26018
[8] Zhang, Shuqin, Existence of solution for a boundary value problem of fractional order, Acta Mathematica scientia series B, 2, 220-228, (2006) · Zbl 1106.34010
[9] Chang, Yong-Kui; Nieto, Juan J., Some new existence results for fractional differential inclusions with boundary conditions, Mathematical and computer modelling, 49, 3-4, 605-609, (2009) · Zbl 1165.34313
[10] Bai, Z.; Lu, H., Positive solutions for boundary value problem of nonlinear fractional differential equation, Journal of mathematical analysis and applications, 311, 495-505, (2005) · Zbl 1079.34048
[11] Guo, D.; Lakshmikantham, V., Coupled fixed points of nonlinear operators with applications, Nonlinear analysis, 11, (1987), 623-C632 · Zbl 0635.47045
[12] Guo, D.; Lakshmikantham, V., Nonlinear problems in abstract cones, (1988), Academic Press New York · Zbl 0661.47045
[13] Guo, D., Existence and uniqueness of positive fixed point for mixed monotone operators with applications, Applicable analysis, 46, (1992), 91-C100 · Zbl 0792.47053
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