Agarwal, PriyankaNieto Roig, Juan JoséLuo, M.-J.2018-10-222018-10-222017Agarwal, P., Nieto, J.J., Luo, M.-J. (2017). Extended Riemann-Liouville type fractional derivative operator with applications. Open Mathematics, 15(1), pp. 1667–1681. doi: https://doi.org/10.1515/math-2017-0137http://hdl.handle.net/10347/17585The 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 presentedeng© 2017 Agarwal et al. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 Licensehttp://creativecommons.org/licenses/by-nc-nd/4.0/Gamma functionExtended beta functionRiemann-Liouville fractional derivativeHypergeometric functionsFox H-functionGenerating functionsMellin transformIntegral representationsjournal article10.1515/math-2017-01372391-5455open access