Extended Riemann-Liouville type fractional derivative operator with applications

被引：32
|
作者：
Agarwal, P. [1 ]
Nieto, Juan J. [2 ]
Luo, M. -J. [3 ]
机构：
[1] Anand Int Coll Engn, Dept Math, Jaipur 303012, Rajasthan, India
[2] Univ Santiago de Compostela, Inst Matemat, Dept Estat Anal Matemat & Optimizac, Santiago De Compostela 15782, Spain
[3] East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China
来源：
OPEN MATHEMATICS | 2017年 / 15卷
关键词：
Gamma function; Extended beta function; Riemann-Liouville fractional derivative; Hypergeometric functions; Fox H-function; Generating functions; Mellin transform; Integral representations; INCOMPLETE GAMMA-FUNCTIONS; EXTENSION; BETA;
D O I：
10.1515/math-2017-0137
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The main purpose of this paper is to introduce a class of new extended forms of the beta function, Gauss hypergeometric function and Appell-Lauricella hypergeometric functions by means of the modified Bessel function of the third kind. Some typical generating relations for these extended hypergeometric functions are obtained by defining the extension of the Riemann-Liouville fractional derivative operator. Their connections with elementary functions and Fox's H-function are also presented.
引用
收藏
页码：1667 / 1681
页数：15
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