Extended Riemann-Liouville type fractional derivative operator with applications

Open Mathematics

卷:15

Nieto Juan J.¹  Agarwal P.²  Luo M.-J.³ 

[1] Departamento de Estatística, Análise Matemática e Optimización, Instituto de Matemáticasd, Universidade de Santiago de Compostela, 15782Santiago de Compostela, Spain;

[2] Department of Mathematics, Anand International College of Engineering, Jaipur-303012, Republic of India;

[3] Department of Mathematics, East China Normal University, Shanghai200241, China;

关键词: gamma function;    extended beta function;    riemann-liouville fractional derivative;    hypergeometric functions;    fox h-function;    generating functions;    mellin transform;    integral representations;    26a33;    33b15;    33b20;    33c05;    33c20;    33c65;   

DOI  :  10.1515/math-2017-0137

来源: DOAJ

【 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.

【 授权许可】

Unknown