Research Article

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

Volume: 8 Number: 1 April 15, 2020
EN

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

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.

Keywords

References

  1. [1] S. Belarbi, Z. Dahmani, On some new fractional integral inequalities, JIPAM, 10(3) (2009), 1–9.
  2. [2] M. Bezziou, Z. Dahmani, M.Z. Sarikaya, New operators for fractional integration theory with some applications, J. Math. Extension, In press 2018.
  3. [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. [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. [5] Z. Dahmani, About some integral inequalities using Riemann-Liouville integrals. General Mathematics, 20(4) (2012), 63–69.
  6. [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. [7] S.S. Dragomir: Some integral inequalities of Gr¨uss type,Indian J. Pure Appl. Math. 31 (2002), 397–415.
  8. [8] M. Houas, Z. Dahmani: Random variable inequalities involving (k; s)􀀀integration. Malaya J. Mat., 5(4) (2017), 641–646.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Mohamed Bezzıou This is me
Algeria

Publication Date

April 15, 2020

Submission Date

December 17, 2019

Acceptance Date

April 17, 2020

Published in Issue

Year 2020 Volume: 8 Number: 1

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. https://izlik.org/JA95GL59YZ
AMA
1.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. https://izlik.org/JA95GL59YZ
Chicago
Bezzıou, Mohamed, Zoubir Dahmani, and Mehmet Eyüp Kiriş. 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. https://izlik.org/JA95GL59YZ.
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
[1]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, Apr. 2020, [Online]. Available: https://izlik.org/JA95GL59YZ
ISNAD
Bezzıou, Mohamed - Dahmani, Zoubir - Kiriş, Mehmet Eyüp. “Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities”. Konuralp Journal of Mathematics 8/1 (April 1, 2020): 197-206. https://izlik.org/JA95GL59YZ.
JAMA
1.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, Apr. 2020, pp. 197-06, https://izlik.org/JA95GL59YZ.
Vancouver
1.Mohamed Bezzıou, Zoubir Dahmani, Mehmet Eyüp Kiriş. Applications of the (k,s,h)-Riemann-Liouville and (k,h)-Hadamard Fractional Operators on Inequalities. Konuralp J. Math. [Internet]. 2020 Apr. 1;8(1):197-206. Available from: https://izlik.org/JA95GL59YZ
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