Submitted:
09 January 2018
Posted:
10 January 2018
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Abstract
Recently, different extensions of the fractional derivative operator are found in many research papers. The main aim of this paper is to establish an extension of the extended Caputo fractional derivative operator. The extension of an extended fractional derivative of some elementary functions derives by considering an extension of beta function which includes the Mittag-Leffler function in the kernel. Further, an extended fractional derivative of some familiar special functions, the Mellin transforms of newly defined Caputo fractional derivative operator and the generating relations for extension of extended hypergeometric functions also presented in this study.
Keywords:
hypergeometric function
; beta function
; extended hypergeometric function
; mellin transform
; fractional derivative
; caputo fractional derivative
; appell's function
; generating relation
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