Existence and uniqueness of positive and nondecreasing solutions for a class of fractional boundary value problems involving the p-Laplacian operator.

In this article, we investigate the existence of a solution arising from the following fractional q-difference boundary value problem by using the p-Laplacian operator: $D_{q}^{\gamma}(\phi_{p}(D_{q}^{\delta}y(t)))+f(t,y(t))=0$ ( $0< t<1$; $0<\gamma<1$; $3<\delta<4$), $y(0)=(D_{q}y)(0)=(D_{q}^{2}y)(0) =0$, $a_{1}(D_{q}y)(1)+a_{2}(D_{q}^{2}y)(1)=0$, $a_{1} +\vert a_{2}\vert \neq0$, $D_{0+}^{\gamma}y(t)|_{t=0}=0$. We make use of such a fractional q-difference boundary value problem in order to show the existence and uniqueness of positive and nondecreasing solutions by means of a familiar fixed point theorem. [ABSTRACT FROM AUTHOR]