Extended Riemann-Liouville type fractional derivative operator with applications

P. Agarwal, Juan J. Nieto, M.-J. Luo
2017 Open Mathematics  
AbstractThe 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
doi:10.1515/math-2017-0137 fatcat:ymfgrfeaczf73gre73fif32f2q