The Prabhakar Fractional q-Integral and q-Differential Operators

In this short note, we discuss the joint work (Shaimardan et al., The Prabhakar fractional q-integral and q-differential operators, and their properties, 2022. arXiv:2212.08843) with E. Karimov and M. Ruzhansky. More specifically, we give the definitions and the main properties of the Prabhakar fractional q-integral and q-differential operators. More precisely, we present the semigroup 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. Moreover, we give the result on the boundness of the Prabhakar fractional q-integral operator in the class of q-integrable functions.