Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities
This paper deals with some results of fractional inequalities involving two recent recent integral operators: the $\left( k,s,h\right) -$Riemann-Liouville integral and the $\left( k,h\right)-$Hadamard fractional operator. We generalize some classical integral inequalities as well as some other fractional inequalities. By simple arguments, we establish a relation between the two considered operators that allows us to establish several integral results.
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- [1] S. Belarbi, Z. Dahmani, On some new fractional integral inequalities, JIPAM, 10(3) (2009), 1–9.
- [2] M. Bezziou, Z. Dahmani, M.Z. Sarikaya, New operators for fractional integration theory with some applications, J. Math. Extension, In press 2018.
- [3] P.L. Chebyshev, Sur les expressions approximatives des integrales definis par les autres prises entre les memes limite. Proc. Math. Soc. Charkov, 2, (1882), 93–98.
- [4] Z. Dahmani, L. Tabharit, On weighted Gr¨uss type inequalities via fractional integrals. Journal of Advanced Research in Pure Mathematics, 2(4) (2010), 31–38.
- [5] Z. Dahmani, About some integral inequalities using Riemann-Liouville integrals. General Mathematics, 20(4) (2012), 63–69.
- [6] Z. Dahmani, L. Tabharit, S. Taf: New generalizations of Gr¨uss inequality using Riemann-Liouville fractional integrals. Belletin of Mathematical Analysis and applications, 2 (3) (2010), 93–99.
- [7] S.S. Dragomir: Some integral inequalities of Gr¨uss type,Indian J. Pure Appl. Math. 31 (2002), 397–415.
- [8] M. Houas, Z. Dahmani: Random variable inequalities involving (k; s)?integration. Malaya J. Mat., 5(4) (2017), 641–646.
- [9] P. Kumar: Inequality involving moments of a continuous random variable defined over a finite interval, Computers and Mathematics with Applications, 48 (2004), 257–273.
- [10] M. Z. Sarikaya, H. Yaldiz: New generalization fractional inequalities of Ostrowski-Gr¨uss type. Lobachevskii Journal of Mathematics, 34(4) (2013), 326–331.
- [11] M. Z. Sarikaya, N. Aktan, H. Yildirim: On weighted Chebyshev-Gr¨uss like inequalities on time scales. J. Math. Inequal, 2(2) (2008), 185–195.
- [12] E. Set, M. Tomar and M.Z. Sarikaya: On generalization Gr¨uss type inequalities for k?fractional integrals. Applied Mthematics and Computation, 269 (2015), 29–34.
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2013
- Yayıncı: Mehmet Zeki SARIKAYA