The terminology "best method" is a confusing word, because I think, in what context it is physically quantified, is very relevant.
One of the efficient methods, however, for your own case of the fractional NLS and like systems to be exactly integrated may be the "methods of fractional steps". The details may be found at the following book:
N. N. Yanenko, The method of fractional steps, Springer, N. Y., 1971.
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