Summary: In this article, we study the fractional \(q\)-difference boundary-value problems with \(p\)-Laplacian operator \[ \begin{aligned} D_q^\gamma(\phi_p & (D_q^\alpha u(t)))+f(t,u(t))=0,\quad 0<t<1,\quad 2<\alpha<3,\\ & u(0)=(D_qu)(0)=0,\quad (D_qu)(1)=\beta(D_qu)(\eta),\end{aligned} \] where \(0<\gamma<1\), \(2<\alpha<3\), \(0<\beta\eta^{\alpha-2}<1\), \(D_{0+}^\alpha\) is the Riemann-Liouville fractional derivative, \(\phi_p(s)=|s|^{p-2}s\), \(p>1\). By using a fixed-point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solutions.