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Existence and uniqueness of positive solutions to m-point boundary value problem for nonlinear fractional differential equation

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Abstract

In this paper, we consider the following nonlinear fractional m-point boundary value problem

where \(D_{0+}^{\alpha}\) is the standard Riemann-Liouville fractional derivative. By the properties of the Green function, the lower and upper solution method and fixed-point theorem in partially ordered sets, some new existence and uniqueness of positive solutions to the above boundary value problem are established. As applications, examples are presented to illustrate the main results.

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Authors and Affiliations

  1. College of Mathematics, Changchun Normal University, Changchun, 130032, Jilin, PR China

    Sihua Liang

  2. Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Nanjing, 210046, Jiangsu, PR China

    Jihui Zhang

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  1. Sihua Liang
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  2. Jihui Zhang
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Correspondence to Sihua Liang.

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Liang, S., Zhang, J. Existence and uniqueness of positive solutions to m-point boundary value problem for nonlinear fractional differential equation. J. Appl. Math. Comput. 38, 225–241 (2012). https://doi.org/10.1007/s12190-011-0475-2

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  • DOI: https://doi.org/10.1007/s12190-011-0475-2

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