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Certain q-Kober fractional integral operator of generalized basic hypergeometric functions and q-polynomials

Authors

Jayprakash Yadav
Type: Article
Publication Date: 2025-04-29
Citations: 0
DOI: https://doi.org/10.47191/ijmcr/v13i4.14

Abstract

The object of this paper is to established the Kober fractional integral operator of the generalized basic hypergeometric function.Interestingly Kober fractional integral operator of various q-polynomials have been expressed in terms of the basic analogue of Kamp˙e de F˙eriet function.Some special cases have been deduced as an application of main result.

Topics

Locations

  • INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH
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The object of this paper is to establish transformations in which a basic hypergeometric functions can be expressed as an infinite sum of functions of higher order by the application … The object of this paper is to establish transformations in which a basic hypergeometric functions can be expressed as an infinite sum of functions of higher order by the application of fractional q-differential operator.Several well known hypergeometric functions and basic Kamp˙ e de F˙eriet function are expressed as an infinite sum of basic hypergeometric functions.Some special cases can be deduced as the application of the main results.

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In this paper the operator L(.) of the basic multiple hypergeometric function given by Yadav et al. is used in order to obtain the fractional q-integral operator L(.) of the … In this paper the operator L(.) of the basic multiple hypergeometric function given by Yadav et al. is used in order to obtain the fractional q-integral operator L(.) of the generalized basic hypergeometric function rs (.), also the q-Mellin transform for the operator L(.) is presented. Various interesting special cases, involving q-special functions, have been derived as application of the main result.

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In the present paper, we obtain q-analogues of Saigo fractional integrals and deriva- tives of generalized basic hypergeometric series. Similar results for some simpler functions and polynomials have also been … In the present paper, we obtain q-analogues of Saigo fractional integrals and deriva- tives of generalized basic hypergeometric series. Similar results for some simpler functions and polynomials have also been derived as special cases of our main findings.

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