Extended Riemann-Liouville fractional derivative operator and its applications

Volume 8, Issue 5, pp 451--466 http://dx.doi.org/10.22436/jnsa.008.05.01

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Authors

Praveen Agarwal - Department of Mathematics, Anand International College of Engineering, Jaipur-303012, India. Junesang Choi - Department of Mathematics, Dongguk University, Gyeongju 780-714, 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 Riemann-Liouville 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.

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Keywords

• Gamma function
• Beta function
• Riemann-Liouville fractional derivative
• hypergeometric functions
• fox H-function
• generating functions
• Mellin transform
• integral representations.

MSC

•  26A33
•  33C05
•  33C20
•  33C65

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