In this paper approximations of three classes of fractional derivatives (FD)
using modified Gauss integration (MGI) and Gauss-Laguerre integration (GLI) are
considered. The main solutions of these fractional derivatives depend on
inverse of Laplace transforms, which are handled by these procedures. In the
modified form of integration the weights and nodes are obtained by means of a
difference equation, which gives a proper approximation form for the inverse of
Laplace transform and hence the fractional derivatives.