In this paper, we study on the new class of q-fractional integral operator. In the aid of iterated Cauchy integral approach to fractional integral operator, we applied tp f(t) in… Click to show full abstract
In this paper, we study on the new class of q-fractional integral operator. In the aid of iterated Cauchy integral approach to fractional integral operator, we applied tp f(t) in these integrals and a new class of q-fractional integral operator with parameter p, is introduced. Recently, the q-analogue of fractional differential integral operator is studied and all of the operators defined in these studies are q-analogue of Riemann fractional differential operator. We show that our new class of operator generalize all the operators in use, and additionally, it can cover the q-analogue of Hadamard fractional differential operator, as well. Some properties of this operator are investigated.
               
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