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Year 2020, Volume: 8 Issue: 1, 197 - 206, 15.04.2020
https://izlik.org/JA95GL59YZ

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
https://izlik.org/JA95GL59YZ

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 Research Article
Authors

Mohamed Bezzıou This is me

Zoubir Dahmani

Mehmet Eyüp Kiriş

Submission Date December 17, 2019
Acceptance Date April 17, 2020
Publication Date April 15, 2020
IZ https://izlik.org/JA95GL59YZ
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. 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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