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In this article, we study the existence of positive solutions for the singular fractional boundary value problem $$\displaylines{ - D^\alpha u(t) = A f (t, u (t))+\sum_{i=1}^k B_i I^{\beta_i} g_i (t, u(t)) , \quad t \in (0, 1),\cr D^\delta u (0) = 0,\quad D^\delta u (1) = a D^{\frac{\alpha-\delta-1}{2}}(D^\delta u (t))\big|_{t=\xi} }$$ where $1<\alpha\leq 2$, $0<\xi \leq 1/2$, $a \in [0,\infty)$, $1<\alpha-\delta <2$, $0<\beta_i< 1$, $A,B_i$, $1\leq i \leq k$, are real constant, $D^\alpha$ is the Riemann-Liouville fractional derivative of order $\alpha$. By using the Banach's fixed point theorem and Leray-Schauder's alternative, the existence of positive solutions is obtained. At last, an example is given for illustration.