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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:
34B15Nonlinear boundary value problems for ODE
26A33Fractional derivatives and integrals (real functions)
34A08Fractional differential equations
45J05Integro-ordinary differential equations
References:
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[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, No. 2, 565-572 (2009) · Zbl 1176.34070 · doi:10.1016/j.cam.2008.05.033
[4]Benchohra, M.; Hamania, S.; Ntouyas, S. K.: Boundary value problems for differential equations with fractional order and nonlocal conditions, Nonlinear analysis 71, No. 7–8, 2564-2575 (2009) · Zbl 1198.26007 · doi:10.1016/j.na.2009.01.073
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[8]Zhang, Shuqin: Existence of solution for a boundary value problem of fractional order, Acta Mathematica scientia series B, No. 2, 220-228 (2006) · Zbl 1106.34010 · doi:10.1016/S0252-9602(06)60044-1
[9]Chang, Yong-Kui; Nieto, Juan J.: Some new existence results for fractional differential inclusions with boundary conditions, Mathematical and computer modelling 49, No. 3–4, 605-609 (2009) · Zbl 1165.34313 · doi:10.1016/j.mcm.2008.03.014
[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 · doi:10.1016/j.jmaa.2005.02.052
[11]Guo, D.; Lakshmikantham, V.: Coupled fixed points of nonlinear operators with applications, Nonlinear analysis 11 (1987) · Zbl 0635.47045 · doi:10.1016/0362-546X(87)90077-0
[12]Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones, (1988)
[13]Guo, D.: Existence and uniqueness of positive fixed point for mixed monotone operators with applications, Applicable analysis 46 (1992) · Zbl 0792.47053 · doi:10.1080/00036819208840113