Abstract
In this work, we investigate the following nonlinear singular problem with Riemann-Liouville Fractional Derivative
(P-lambda){-D-t(1)alpha(vertical bar D-0(t)alpha(u(t))vertical bar(p-2) (0)D(t)(alpha)u(t)) = g(t)/u(gamma)(t) + lambda f(t, u(t)) t is an element of (0, T);
u(0) = u(T) = 0,
where lambda is a positive parameter, p > 1, 1/2 < alpha <= 1, 0 < gamma < 1, g is an element of C([0, T]) and f is an element of C ([0, T] x 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 lambda(0) such that for all( )lambda is an element of (0, lambda(0)) the problem (P-lambda) has at least two positive solutions. Finally, some examples are given to illustrate our results.