Extension of the fractional derivative operator of the Riemann-Liouville

Volume 10, Issue 6, pp 2914--2924 http://dx.doi.org/10.22436/jnsa.010.06.06

Publication Date: June 25, 2017 Submission Date: May 02, 2017

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Authors

Dumitru Baleanu - Department of Mathematics, Cankaya University, Ankara, Turkey. - Institute of Space Sciences, Magurele-Bucharest, Romania. Praveen Agarwal - Department of Mathematics, Anand International College of Engineering, Jaipur-303012, Republic of India. - Department of Mathematics, University Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia. Rakesh K. Parmar - Department of Mathematics, Govt. College of Engineering and Technology, Bikaner-334004, Rajasthan, India. Maysaa M. Alqurashi - Department of Mathematics, King Saud University, P. O. Box 22452, Riyadh 11495, Saudi Arabia. Soheil Salahshour - Department of Computer Engineering, Mashhad Branch, IAU, Iran.

Abstract

By using the generalized beta function, we extend the fractional derivative operator of the Riemann-Liouville and discusses its properties. Moreover, we establish some relations to extended special functions of two and three variables via generating functions.

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Keywords

• Hypergeometric function of two and three variables
• fractional derivative operator
• generating functions
• Mellin transform.

MSC

•  33C05
•  33C15

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