In this work, we investigate the following nonlinear singular problem with Riemann-Liouville Fractional Derivative (Pλ)  −tDα1 ( |0Dαt (u(t))|p−2 0Dαt u(t) ) = 1(t) uγ(t) + λ f (t,u(t)) t ∈ (0,T); u(0) = u(T) = 0, where λ is a positive parameter, p > 1, 12 < α ≤ 1, 0 < γ < 1, 1 ∈ C([0,T]) and f ∈ C([0,T] × R,R). Under appropriate assumptions on the function f , we employ the method of the Nehari manifold combined with the fibering maps in order to show the existence of λ0 such that for all λ ∈ (0, λ0) the problem (Pλ) has at least two positive solutions. Finally, some examples are given to illustrate our results