  We study the new class of q-fractional integral operator. In the aid of
iterated Cauchy integral approach to fractional integral operator, we applied
t^pf(t) instead of f(t) in these integrals and with parameter p a new class of
q-fractional integral operator is introduced. Recently the q-analogue of
fractional differential integral operator is studied.[8][4][9][10][13][14]All
of these operators are q-analogue of Riemann fractional differential operator.
The new class of introduced operator generalize all these defined operator and
can be cover the q-analogue of Hadamard fractional differential operator. Some
properties of this operator is investigated.
