Extended RiemannLiouville fractional derivative operator and its applications
Authors
Praveen Agarwal
 Department of Mathematics, Anand International College of Engineering, Jaipur303012, India.
Junesang Choi
 Department of Mathematics, Dongguk University, Gyeongju 780714, Republic of Korea.
R. B. Paris
 School of Computing, Engineering and Applied Mathematics, University of Abertay Dundee, Dundee DD1 1HG, UK.
Abstract
Many authors have introduced and investigated certain extended fractional derivative operators. The main
object of this paper is to give an extension of the RiemannLiouville fractional derivative operator with
the extended Beta function given by Srivastava et al. [22] and investigate its various (potentially) useful
and (presumably) new properties and formulas, for example, integral representations, Mellin transforms,
generating functions, and the extended fractional derivative formulas for some familiar functions.
Keywords
 Gamma function
 Beta function
 RiemannLiouville fractional derivative
 hypergeometric functions
 fox Hfunction
 generating functions
 Mellin transform
 integral representations.
MSC
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