Journal of Applied Mathematics and Computing

, Volume 38, Issue 1, pp 225–241

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

Article

DOI: 10.1007/s12190-011-0475-2

Cite this article as:
Liang, S. & Zhang, J. J. Appl. Math. Comput. (2012) 38: 225. doi:10.1007/s12190-011-0475-2

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.

Keywords

Fractional differential equation Partially ordered sets Fixed-point theorem Lower and upper solution method Positive solution 

Mathematics Subject Classification (2000)

26A33 34B18 34B27 

Copyright information

© Korean Society for Computational and Applied Mathematics 2011

Authors and Affiliations

  1. 1.College of MathematicsChangchun Normal UniversityChangchunPR China
  2. 2.Institute of Mathematics, School of Mathematical ScienceNanjing Normal UniversityNanjingPR China

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