An extension of Caputo fractional derivative operator and its applications
Authors
İ. Onur Kıymaz
 Dept. of Mathematics, Ahi Evran Univ., 40100 Kırşehir, Turkey.
Ayşegül Çetinkaya
 Dept. of Mathematics, Ahi Evran Univ., 40100 Kırşehir, Turkey.
Praveen Agarwal
 Dept. of Mathematics, Anand International College of Eng., 303012 Jaipur, India.
Abstract
In this paper, an extension of Caputo fractional derivative operator is introduced, and the extended
fractional derivatives of some elementary functions are calculated. At the same time, extensions of some
hypergeometric functions and their integral representations are presented by using the extended fractional
derivative operator, linear and bilinear generating relations for extended hypergeometric functions are obtained,
and Mellin transforms of some extended fractional derivatives are also determined.
Keywords
 Caputo fractional derivative
 hypergeometric functions
 generating functions
 Mellin transform
 integral representations.
MSC
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