In this paper, we study the problem of existence of positive solution to the following boundary value problem: $D_{0^+}^\sigma  u'' (t) - g (t) f (u (t)) = 0$, $t \in (0, 1)$, $u'' (0) =  u'' (1) = 0$, \, $a u (0) - b u' (0) = \sum_{i = 1}^{m - 2} a_i u (\xi_i)$, \, $c u (1) + d u' (1) = \sum_{i = 1}^{m - 2} b_i u (\xi_i)$, where $D_{0^+}^\sigma$ is the Riemann-Liouville fractional derivative of order $1 < \sigma \leq 2$ and $f$ is a lower semi-continuous function. Using Krasnoselskii's fixed point theorems in a cone, the existence of one positive solution and multiple positive solutions for nonlinear singular boundary value problems is established.