In this paper, starting from the historical developments of fractional calculus, certain results regarding fractional calculus have been discussed. These
results have been further used to establish transformation formulae for ordinary hypergeometric series as well as for q-hypergeometric series.
Keywords and Phrases
Fractional derivative, fractional q-derivative, transformation formula, hypergeometric series, q-hypergeometric series.
A.M.S. subject classiﬁcation
Primary 11A55, 33D15, 33D90; Secondary 11F20, 33F05.