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.