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Year 2020, Volume: 8 Issue: 1, 197 - 206, 15.04.2020

Abstract

References

  • [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.

Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities

Year 2020, Volume: 8 Issue: 1, 197 - 206, 15.04.2020

Abstract

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.

References

  • [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.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mohamed Bezzıou This is me

Zoubir Dahmani

Mehmet Eyüp Kiriş

Publication Date April 15, 2020
Submission Date December 17, 2019
Acceptance Date April 17, 2020
Published in Issue Year 2020 Volume: 8 Issue: 1

Cite

APA Bezzıou, M., Dahmani, Z., & Kiriş, M. E. (2020). Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities. Konuralp Journal of Mathematics, 8(1), 197-206.
AMA Bezzıou M, Dahmani Z, Kiriş ME. Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities. Konuralp J. Math. April 2020;8(1):197-206.
Chicago Bezzıou, Mohamed, Zoubir Dahmani, and Mehmet Eyüp Kiriş. “Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities”. Konuralp Journal of Mathematics 8, no. 1 (April 2020): 197-206.
EndNote Bezzıou M, Dahmani Z, Kiriş ME (April 1, 2020) Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities. Konuralp Journal of Mathematics 8 1 197–206.
IEEE M. Bezzıou, Z. Dahmani, and M. E. Kiriş, “Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities”, Konuralp J. Math., vol. 8, no. 1, pp. 197–206, 2020.
ISNAD Bezzıou, Mohamed et al. “Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities”. Konuralp Journal of Mathematics 8/1 (April 2020), 197-206.
JAMA Bezzıou M, Dahmani Z, Kiriş ME. Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities. Konuralp J. Math. 2020;8:197–206.
MLA Bezzıou, Mohamed et al. “Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities”. Konuralp Journal of Mathematics, vol. 8, no. 1, 2020, pp. 197-06.
Vancouver Bezzıou M, Dahmani Z, Kiriş ME. Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities. Konuralp J. Math. 2020;8(1):197-206.
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