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Unique positive solutions for fractional differential equation boundary value problems. (English) Zbl 1200.34008
Summary: We consider the uniqueness of positive solutions for fractional differential equation boundary value problems. Our results can not only guarantee the existence of a unique positive solution, but also be applied to construct an iterative scheme for approximating it.
MSC:
34A08Fractional differential equations
34B18Positive solutions of nonlinear boundary value problems for ODE
34A45Theoretical approximation of solutions of ODE
References:
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[4]Ahamed, Bashir; Sivasundaram, S.: Theory of fractional differential equations with three point boundary conditions, Communication in applied analysis 12, 485-489 (2008) · Zbl 1180.34004
[5]Jiang, D.; Yuan, C.: The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application, Nonlinear analysis 72, 710-719 (2010) · Zbl 1192.34008 · doi:10.1016/j.na.2009.07.012
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[7]Ahamed, Bashir; Sivasundaram, S.: Existence and uniqueness results for nonlinear boundary value problem of fractional differential equation with separated boundary conditions, Communication in applied analysis 13, 121-129 (2009) · Zbl 1180.34003
[8]Bai, Z.: On positive solutions of a nonlocal fractional boundary value problem, Nonlinear analysis 72, 916-924 (2010) · Zbl 1187.34026 · doi:10.1016/j.na.2009.07.033
[9]Li, C. F.; Luo, X.; Zhou, Y.: Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations, Computers and mathematics with applications 59, 1363-1375 (2010) · Zbl 1189.34014 · doi:10.1016/j.camwa.2009.06.029
[10]Xu, X.; Jiang, D.; Yuan, Chengjun: Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation, Nonlinear analysis 71, 4676-4688 (2009) · Zbl 1178.34006 · doi:10.1016/j.na.2009.03.030
[11]Zhang, S.: Positive solutions to singular boundary value problem for nonlinear fractional differential equation, Computers and mathematics with applications 59, 1300-1309 (2010) · Zbl 1189.34050 · doi:10.1016/j.camwa.2009.06.034
[12]Wang, W.; Liang, Z.: Fixed point theorem of a class of nonlinear operators and applications, Acta Mathematica sinica 48, 789-800 (2005) · Zbl 1125.47313