Generalized Leibniz rule for an extended fractional derivative operator with applications to special functions
Yükleniyor...
Tarih
2011
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Selcuk University Research Center of Applied Mathematics
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Recently an extended operator of fractional derivative related to a generalized beta function has been used in order to obtain some generating relations involving extended hypergeometric functions [19]. In this paper, an extended fractional derivative operator with respect to an arbitrary regular and univalent function based on the Cauchy integral formula is defined. This is done to compute the extended fractional derivative of the function log z and principally, to obtain a generalized Leibniz rule. Some examples involving special functions are given. A representation of the extended fractional derivative operator in terms of the classical fractional derivative operator is also determined by using a result of A.R. Miller [12].
Açıklama
URL: http://sjam.selcuk.edu.tr/sjam/article/view/310
Anahtar Kelimeler
Extended beta function, Fractional derivatives, Extended special functions, Genişletilmiş beta işlevi, Genişletilmiş özel işlevler, Fraksiyonel türevler
Kaynak
Selcuk Journal of Applied Mathematics
WoS Q Değeri
Scopus Q Değeri
Cilt
12
Sayı
Künye
Gaboury, S., Tremblay, R., Fugère, B. J. (2011). Generalized Leibniz rule for an extended fractional derivative operator with applications to special functions. Selcuk Journal of Applied Mathematics, 12 (2), 119-134.
