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Aysel Karaca
Mehmet Zeki Sarikaya*
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Mehmet Zeki Sarikaya*
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International Journal of Statistics and Mathematics IF 2015: 4.232

On the k-Riemann-Liouville fractional integral and applications

Mehmet Zeki Sarikaya and Aysel Karaca

Accepted 30 August, 2014.

Citation: Sarikaya MZ, Karaca A (2014). On the  k-Riemann-Liouvillefractional integral and applications. International Journal of Statistics and Mathematics 1(2): 033-043.

Copyright: © 2014 Sarikaya and Karaca. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Abstract

Fractional calculus is a generalization of ordinary differentiation and integration to arbitrary non-integer order. The subject is as old as differential calculus and goes back to times when G.W. Leibniz and I. Newton invented differential calculus. Fractional integrals and derivatives arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of physics, chemistry, aerodynamics, electrodynamics of a complex medium. Very recently, Mubeen and Habibullah have introduced the k-Riemann-Liouville fractional integral defined by using the -Gamma function, which is a generalization of the classical Gamma function. In this paper, we presents a new fractional integration is called k-Riemann-Liouville fractional integral, which generalizes the k-Riemann-Liouville fractional integral. Then, we prove the commutativity and the semi-group properties of the -Riemann-Liouville fractional integral and we give Chebyshev inequalities for k-Riemann-Liouville fractional integral. Later, using k-Riemann-Liouville fractional integral, we establish some new integral inequalities.

Keywords: Riemann-liouville fractional integral, convex function, hermite-hadamard inequality and hölder's inequality.

Mathematics Subject Classification: 26A33;26A51;26D15.

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