ON HADAMARD-TYPE INEQUALITIES FOR $k$-FRACTIONAL INTEGRALS

Abstract

In this paper we prove Hadamard-type inequalities for $k$-fractional Riemann-Liouville integrals and Hadamard-type inequalities for fractional Riemann-Liouville integrals are deduced. Also we deduced some well known results related to Hadamard inequality.

Keywords

• Convex functions,Hadamard inequalities,fractional integral

References

1. [1] R. Diaz, E. Pariguan, On hypergeometric functions and pochhammer k-symbol, Divulg. Mat. Vol:15, No.2 (2007), 179{192.
2. [2] M. Dalir, M. Bashour, Applications of fractional calculus, Appl. Math. Sci. Vol:4, No.21 (2010), 1021{1032.
3. [3] R. Goren o, F. Mainardi, Fractional Calculus: integral and dierential equations of fractional order, Springer Verlag, Wien, 1997, 223-276.
4. [4] A. Loverro, Fractional Calculus: History, Denitions and Applications for the Engineer, Department of Aerospace and Mechanical Engineering, University of Notre Dame, 2004.
5. [5] S. Mubeen, G. M. Habibullah, k-Fractional integrals and applications, Int. J. Contemp. Math. Sci. Vol:7 (2012), 89{94.
6. [6] S. Miller, B. Ross, An introduction to fractional calculus and fractional differential equations, John Wiley And Sons, Usa, 1993.
7. [7] I. Podlubni, Fractional dierential equations, Academic Press, San Diego, 1999.
8. [8] M. Z. Sarikaya, H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals, RGMIA Research Report Collection, 17 (2014), Article 98, 10 pp.