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


Gürel Yılmaz Ö. , Aktaş R., Taşdelen Yeşildal F.

FRACTAL AND FRACTIONAL, vol.4, no.4, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.3390/fractalfract4040048
  • Title of Journal : FRACTAL AND FRACTIONAL
  • Keywords: k-gamma function, k-beta function, Pochhammer symbol, hypergeometric function, Appell functions, integral representation, reduction and transformation formula, fractional derivative, generating function, HYPERGEOMETRIC-FUNCTIONS, OPERATORS

Abstract

Our present investigation is mainly based on the k-hypergeometric functions which are constructed by making use of the Pochhammer k-symbol in Diaz et al. 2007, which are one of the vital generalizations of hypergeometric functions. In this study, we focus on the k-analogue of F-1 Appell function introduced by Mubeen et al. 2015 and the k-generalizations of F-2 and F-3 Appell functions indicated in Kiymaz et al. 2017. 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. 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.