On some formulas for the K-analogue of appell functions and generating relations via K-fractional derivative

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 F2 and F3 Appell functions denoted by the symbols F2,k and F3,k, respectively, just like Mubeen et al. did for F1 in 2015. Meanwhile, we prove integral representations of the k-generalizations of F2 and F3 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. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.