The Prabhakar fractional q-integral and q-differential operators, and their properties
Abstract
In this paper, we have introduced the Prabhakar fractional q-integral and q-differential operators. We first study the semi-group property of the Prabhakar fractional q-integral operator, which allowed us to introduce the corresponding q-differential operator. Formulas for compositions of q-integral and q-differential operators are also presented. We show the boundedness of the Prabhakar fractional q-integral operator in the class of q-integrable functions.
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