  We define a general scheme for the evolution of fragmentation functions which
resums soft gluon logarithms in a manner consistent with fixed order evolution.
We present an explicit example of our approach in which double logarithms are
resummed using the Double Logarithmic Approximation. We show that this scheme
reproduces the Modified Leading Logarithm Approximation in certain limits, and
find that after using it to fit quark and gluon fragmentation functions to
experimental data,a good description of the data from the largest x values to
the peak region in ln (1/x) is obtained. In addition, we develop a treatment of
hadron mass effects which gives additional improvements at small x.
