Extended Riemann-Liouville type fractional derivative operator with applications

P. Agarwal, Juan J. Nieto, and M.-J. Luo. "Extended Riemann-Liouville type fractional derivative operator with applications." Open Mathematics 15.1 (2017): 1667-1681. <http://eudml.org/doc/288473>.

@article{P2017,
abstract = {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.},
author = {P. Agarwal, Juan J. Nieto, M.-J. Luo},
journal = {Open Mathematics},
keywords = {Gamma function; Extended beta function; Riemann-Liouville fractional derivative; Hypergeometric functions; Fox H-function; Generating functions; Mellin transform; Integral representations},
language = {eng},
number = {1},
pages = {1667-1681},
title = {Extended Riemann-Liouville type fractional derivative operator with applications},
url = {http://eudml.org/doc/288473},
volume = {15},
year = {2017},
}

TY - JOUR
AU - P. Agarwal
AU - Juan J. Nieto
AU - M.-J. Luo
TI - Extended Riemann-Liouville type fractional derivative operator with applications
JO - Open Mathematics
PY - 2017
VL - 15
IS - 1
SP - 1667
EP - 1681
AB - 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.
LA - eng
KW - Gamma function; Extended beta function; Riemann-Liouville fractional derivative; Hypergeometric functions; Fox H-function; Generating functions; Mellin transform; Integral representations
UR - http://eudml.org/doc/288473
ER -