Journal of Applied Mathematics and Computing

, Volume 40, Issue 1–2, pp 277–288 | Cite as

Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q-differences

Applied mathematics

Abstract

In this paper, we consider the following nonlinear q-fractional three-point boundary value problem
$$\begin{array}{l}(D_{q}^{\alpha}u)(t) + f(t,u(t))=0, \quad 0 < t < 1, 2 < \alpha< 3,\\ [2pt]u(0) = (D_qu)(0) = 0, \quad(D_qu)(1) = \beta(D_qu)(\eta),\end{array}$$
where 0<βηα-2<1. By using a fixed-point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solutions to the above boundary value problem.

Keywords

Fractional q-difference equations Partially ordered sets Fixed-point theorem Positive solution 

Mathematics Subject Classification

39A13 34B18 34A08 

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Copyright information

© Korean Society for Computational and Applied Mathematics 2012

Authors and Affiliations

  1. 1.College of MathematicsChangchun Normal UniversityChangchunPR China
  2. 2.Jiangsu Key Laboratory for NSLSCS, School of Mathematical SciencesNanjing Normal UniversityNanjingPR China

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