  The paper enhances the accuracy of the one-dimensional fractional Fourier
transform (FRFT) using the closed Newton Cotes quadrature rules. Given the
weights generated by the Composite Newton Cotes rules of order QN, it is shown
that a FRFT of a QN-long weighted sequence can be written as two composites of
FRFTs. The first composite of FRFTs is made up of a FRFT of a Q-long weighted
sequence and a FRFT of a N-long sequence. The second composite is made up of a
FRFT of a N-long weighted sequence and a FRFT of a Q-long sequence. The
Empirical evidence suggests that the composite FRFTs has commutative property
and works both algebraically and numerically. The composite of FRFTs is applied
to the problem of inverting Fourier and Laplace transforms. The results show
that the composite FRFTs outperforms both the simple non-weighted FRFT and the
Newton-Cotes integration method, but the difference is less significant for the
integration method.
