The Prabhakar fractional $q$-integral and $q$-differential operators, and their properties
Analysis of PDEs
2022-12-20 v1
Abstract
In this paper, we have introduced the Prabhakar fractional -integral and -differential operators. We first study the semi-group property of the Prabhakar fractional -integral operator, which allowed us to introduce the corresponding -differential operator. Formulas for compositions of -integral and -differential operators are also presented. We show the boundedness of the Prabhakar fractional -integral operator in the class of -integrable functions.
Keywords
Cite
@article{arxiv.2212.08843,
title = {The Prabhakar fractional $q$-integral and $q$-differential operators, and their properties},
author = {Serikbol Shaimardan and Erkinjon Karimov and Michael Ruzhansky and Azizbek Mamanazarov},
journal= {arXiv preprint arXiv:2212.08843},
year = {2022}
}