The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel. We also give some results related to the newly defined fractional operator, such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.
Hypergeometric function, extended hypergeometric function, Mellin transform, fractional derivative, Appell's function
BOHNER, MARTIN; RAHMAN, GAUHAR; MUBEEN, SHAHID; and NISAR, KOTTAKKARAN
"A further extension of the extended Riemann-Liouville fractional derivative operator,"
Turkish Journal of Mathematics: Vol. 42:
5, Article 40.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss5/40