IJSM Navigation
Publication Ethics
Call For Paper
Guide to Authors
Editorial Board
Submit Manuscript
Viewing Options
[View Abstract]
[View Full Text PDF]
[View Full Text PDF]
Authors Articles on Google Scholar
Aysel Karaca
Mehmet Zeki Sarikaya*
Authors Articles on Pubmed
Aysel Karaca
Mehmet Zeki Sarikaya*
Email this Article to a friend
Print this Article
Viewed: 1,062
Forwarded: 0
Printed: 240
Downloaded: 2,776
Browse Journals By Category
Agriculture and Food Sciences
Biological Sciences
Education and Arts
Environmental Sciences
Medical Sciences
Pharmaceutical Sciences
Physical and Natural Sciences
Social Sciences

Newsletters Subscription

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.


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.

Related Articles