On a new class of q-fractional integral operators involving multivariate q-Mittag-Leffler functions
Abstract
Fractional integral operators involving special functions as kernels have long been one of the main subjects of fractional calculus. As a discrete version of classical fractional calculus, q-fractional calculus not only brings often new phenomena and new perspectives but also provides new useful areas for describing and studying new problems of applied nature. Recently, Luo and Zhou (see below) developed a methodology for formulating well-behaved q-fractional integral operators steming from a basic general theory. Our aim in this paper is to define and introduce a new class of q-fractional integral operators whose kernel involves a new multivariate q-Mittag-Leffler function. We shall also define the corresponding q-fractional derivatives (as the inverses of q-fractional integral operators) and define also the q-Caputo fractional derivative operators. We discuss in detail the similarities and variations between the q-operators and their counterparts in classical theory, particularly in Prabakar fractional calculus. Further, applications of the defined operators in solving certain q-fractional differential equations are also considered. We also mention throughout this paper some useful relevances of our established results with certain known important cases. In the concluding remarks, we point out briefly few possible proposals (or directions) for further work on the present subject matter of q-calculus.
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BibTeX
@misc{luo2026class,
title = {{On a new class of $q$-fractional integral operators involving multivariate $q$-Mittag-Leffler functions}},
author = {Min-Jie Luo and Qing-Hui Peng and Ravinder Krishna Raina},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10574},
eprint = {2610.10574},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10574},
}
RIS
TY - UNPB
TI - On a new class of q-fractional integral operators involving multivariate q-Mittag-Leffler functions
AU - Min-Jie Luo
AU - Qing-Hui Peng
AU - Ravinder Krishna Raina
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.10574
UR - https://arxiv.org/abs/2610.10574
AB - Fractional integral operators involving special functions as kernels have long been one of the main subjects of fractional calculus. As a discrete version of classical fractional calculus, q-fractional calculus not only brings often new phenomena and new perspectives but also provides new useful areas for describing and studying new problems of applied nature. Recently, Luo and Zhou (see below) developed a methodology for formulating well-behaved q-fractional integral operators steming from a basic general theory. Our aim in this paper is to define and introduce a new class of q-fractional integral operators whose kernel involves a new multivariate q-Mittag-Leffler function. We shall also define the corresponding q-fractional derivatives (as the inverses of q-fractional integral operators) and define also the q-Caputo fractional derivative operators. We discuss in detail the similarities and variations between the q-operators and their counterparts in classical theory, particularly in Prabakar fractional calculus. Further, applications of the defined operators in solving certain q-fractional differential equations are also considered. We also mention throughout this paper some useful relevances of our established results with certain known important cases. In the concluding remarks, we point out briefly few possible proposals (or directions) for further work on the present subject matter of q-calculus.
ER -