Journal of Applied Mathematics and Computing

, Volume 40, Issue 1–2, pp 277–288

# 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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