Certain q-Analogue of Fractional Integrals and Derivatives Involving Basic Analogue of the Several Variable Aleph-Function
Using Mellin-Barnes contour integrals, we aim at suggesting a q-analogue (q-extension) of the several variable Aleph-function. Then we present Riemann Liouville fractional q-integral and q-differential formulae for the q-extended several variable Aleph-function. Using the q-analogue of the Leibniz r...
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| Vydáno v: | Axioms Ročník 12; číslo 1; s. 51 |
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| Abstract | Using Mellin-Barnes contour integrals, we aim at suggesting a q-analogue (q-extension) of the several variable Aleph-function. Then we present Riemann Liouville fractional q-integral and q-differential formulae for the q-extended several variable Aleph-function. Using the q-analogue of the Leibniz rule for the fractional q-derivative of a product of two basic functions, we also provide a formula for the q-extended several variable Aleph-function, which is expressed in terms of an infinite series of the q-extended several variable Aleph-function. Since the three main formulas presented in this article are so general, they can be reduced to yield a number of identities involving q-extended simpler special functions. In this connection, we choose only one main formula to offer some of its particular instances involving diverse q-extended special functions, for example, the q-extended I-function, the q-extended H-function, and the q-extended Meijer’s G-function. The results presented here are hoped and believed to find some applications, in particular, in quantum mechanics. |
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| AbstractList | Using Mellin-Barnes contour integrals, we aim at suggesting a q-analogue (q-extension) of the several variable Aleph-function. Then we present Riemann Liouville fractional q-integral and q-differential formulae for the q-extended several variable Aleph-function. Using the q-analogue of the Leibniz rule for the fractional q-derivative of a product of two basic functions, we also provide a formula for the q-extended several variable Aleph-function, which is expressed in terms of an infinite series of the q-extended several variable Aleph-function. Since the three main formulas presented in this article are so general, they can be reduced to yield a number of identities involving q-extended simpler special functions. In this connection, we choose only one main formula to offer some of its particular instances involving diverse q-extended special functions, for example, the q-extended I-function, the q-extended H-function, and the q-extended Meijer’s G-function. The results presented here are hoped and believed to find some applications, in particular, in quantum mechanics. |
| Author | Kumar, Dinesh Ayant, Frédéric Choi, Junesang Südland, Norbert |
| Author_xml | – sequence: 1 givenname: Dinesh orcidid: 0000-0001-5415-1777 surname: Kumar fullname: Kumar, Dinesh – sequence: 2 givenname: Frédéric surname: Ayant fullname: Ayant, Frédéric – sequence: 3 givenname: Norbert surname: Südland fullname: Südland, Norbert – sequence: 4 givenname: Junesang orcidid: 0000-0002-7240-7737 surname: Choi fullname: Choi, Junesang |
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| Snippet | Using Mellin-Barnes contour integrals, we aim at suggesting a q-analogue (q-extension) of the several variable Aleph-function. Then we present Riemann... |
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| SubjectTerms | Calculus Fractional calculus fractional q-calculus Identities Infinite series Integrals Mellin-Barnes contour integrals q-Leibniz rule q-several variable Aleph-function q-several variable I-function Quantum mechanics |
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| Title | Certain q-Analogue of Fractional Integrals and Derivatives Involving Basic Analogue of the Several Variable Aleph-Function |
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