摘要：In this study, we discuss the existence of positive solutions for the system of m-singular sum fractional q-differential equations$$ \begin{gathered} D_{q}^{\alpha_{i}} x_{i} + g_{i} \bigl(t, x_), \ldots, x_{m}, D_{q}^{\gamma _)} x_), \ldots, D_{q}^{\gamma_{m}} x_{m} \bigr) \\ \quad{} +h_{i} \bigl(t, x_), \ldots, x_{m}, D_{q}^{\gamma_)} x_), \ldots, D_{q}^{\gamma_{m}} x_{m} \bigr)=0 \end{gathered} $$ with boundary conditions $x_{i}(0) = x_{i}' (1) = 0$ and $x_{i}^{(k)}(t) = 0$ whenever $t=0$, here $2\leq k \leq n-1$, where $n= [\alpha_{i}]+ 1$, $\alpha_{i} \geq2$, $\gamma_{i} \in(0,1)$, $D_{q}^{\alpha}$ is the Caputo fractional q-derivative of order α, here $q \in(0,1)$, function $g_{i}$ is of Carathéodory type, $h_{i}$ satisfy the Lipschitz condition and $g_{i} (t , x_), \ldots, x_{2m})$ is singular at $t=0$, for $1 \leq i \leq m$. By means of Krasnoselskii’s fixed point theorem, the Arzelà-Ascoli theorem, Lebesgue dominated theorem and some norms, the existence of positive solutions is obtained. Also, we give an example to illustrate the primary effects.
