An extension of Caputo fractional derivative operator and its applications

Volume 9, Issue 6, pp 3611--3621 http://dx.doi.org/10.22436/jnsa.009.06.14

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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.

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Keywords

• Caputo fractional derivative
• hypergeometric functions
• generating functions
• Mellin transform
• integral representations.

MSC

•  26A33
•  33C05
•  33C20
•  33C65

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