NDLI: On Some Formulas for the k-Analogue of Appell Functions and Generating Relations via k-Fractional Derivative

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On Some Formulas for the k-Analogue of Appell Functions and Generating Relations via k-Fractional Derivative

Content Provider	MDPI
Author	Rabia, Aktaş Fatma, Taşdelen Yılmaz, Övgü Gürel
Copyright Year	2020
Abstract	Our present investigation is mainly based on the k-hypergeometric functions which are constructed by making use of the Pochhammer k-symbol Diaz et al. 2017, which are one of the vital generalizations of hypergeometric functions. We introduce k-analogues of $F_{2}$ and $F_{3}$ Appell functions denoted by the symbols $F_{2, k}$ and $F_{3, k},$ respectively, just like Mubeen et al. did for $F_{1}$ in 2015. Meanwhile, we prove integral representations of the k-generalizations of $F_{2}$ and $F_{3}$ which provide us with an opportunity to generalize widely used identities for Appell hypergeometric functions. In addition, we present some important transformation formulas and some reduction formulas which show close relation not only with k-Appell functions but also with k-hypergeometric functions. Finally, employing the theory of Riemann–Liouville k-fractional derivative from Rahman et al. 2020, and using the relations which we consider in this paper, we acquire linear and bilinear generating relations for k-analogue of hypergeometric functions and Appell functions.
Starting Page	48
e-ISSN	25043110
DOI	10.3390/fractalfract4040048
Journal	Fractal and Fractional
Issue Number	4
Volume Number	4
Language	English
Publisher	MDPI
Publisher Date	2020-09-24
Access Restriction	Open
Subject Keyword	Fractal and Fractional Hardware and Architecturee Telecommunications K-gamma Function K-beta Function Pochhammer Symbol Hypergeometric Function Appell Functions Integral Representation Reduction and Transformation Formula Fractional Derivative Generating Function
Content Type	Text
Resource Type	Article

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