On Fractional q-Integral Operators Involving the Basic Analogue of Multivariable Aleph-Function

In the present article, we proposed the fractional-order Kober and generalized Weyl q-integrals involving a basic (or q-) analogue of multivariable Aleph-function. Similar assertions for the Riemann-Liouville and Weyl fractional q-integral transforms are also presented. Several corollaries are also established to strengthen the results. By specializing the various parameters and variables in the basic analogue of multivariable Aleph-function, we can obtain a large number of results involving a remarkably wide variety of useful basic functions.

Automated summary

In this article, we introduce the concepts of fractional-order Kober and generalized Weyl q-integrals, as well as present the properties and results of Riemann-Liouville and Weyl fractional q-integral transforms. By specializing variables and parameters, a wide variety of useful basic functions can be obtained.