×

zbMATH — the first resource for mathematics

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.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations and fractional differential inclusions
45J05 Integro-ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
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.