On Some Formulas for the k-Analogue of Appell Functions and Generating Relations via k-Fractional Derivative
FRACTAL AND FRACTIONAL, cilt.4, sa.4, 2020 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 4 Sayı: 4
- Basım Tarihi: 2020
- Doi Numarası: 10.3390/fractalfract4040048
- Dergi Adı: FRACTAL AND FRACTIONAL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: 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
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Ankara Üniversitesi Adresli: Evet
Özet
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.