Compactness of Riemann-Liouville fractional integral operators

We obtain results on compactness of two linear Hammerstein integral operators with singularities, and apply the results to give new proof that Riemann-Liouville fractional integral operators of order alpha is an element of (0,1) map L-p(0,1) to C[0,1] and are compact for each p is an element of ( 1/1-alpha, infinity]. We show that the spectral radii of the Riemann-Liouville fractional operators are zero.