Extended Riemann-Liouville type fractional derivative operator with applications

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URI: http://hdl.handle.net/10347/17585
E-ISSN: 2391-5455
DOI: 10.1515/math-2017-0137

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2017

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De Gruyter
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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

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Gamma function| Extended beta function| Riemann-Liouville fractional derivative| Hypergeometric functions| Fox H-function| Generating functions| Mellin transform| Integral representations

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Agarwal, 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-2017-0137

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The research of J.J. Nieto has been partially supported by the Ministerio de Economía y Competitividad of Spain under grants MTM2016–75140–P, MTM2013–43014–P, Xunta de Galicia, Grants GRC2015-004 and R2016-022, and co- nanced by the European Community fund FEDER

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© 2017 Agarwal et al. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License

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Estatística, Análise Matemática e Optimización