Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

GENERALIZING HARDY TYPE INEQUALITIES VIA k-RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL OPERATORS INVOLVING TWO ORDERS

  • Benaissa, Bouharket (Laboratory of Informatics and Mathematics, Faculty of Material Sciences, University of Tiaret-Algeria)
  • Received : 2022.02.05
  • Accepted : 2022.03.31
  • Published : 2022.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this study, We have applied the right operator k-Riemann-Liouville is involving two orders α and β with a positive parameter p > 0, further, the left operator k-Riemann-Liouville is used with the negative parameter p < 0 to introduce a new version related to Hardy-type inequalities. These inequalities are given and reversed for the cases 0 < p < 1 and p < 0. We then improved and generalized various consequences in the framework of Hardy-type fractional integral inequalities.

Keywords

Acknowledgement

The author also thank the anonymous referees for their valuable comments and suggestions which lead to the final version of this paper. This work was supported by the Directorate-General for Scientific Research and Technological Development (DGRSDT)-Algeria.

References

  1. T. A. Aljaaidi, D. B. Pachpatte, M. S. Abdo, T. Botmart, H. Ahmad, M. A. Almalahi, and S. S. Redhwan., (k, µ)-Proportional Fractional Integral PolyaSzeg- and Gruss-Type Inequalities, Fractal Fract. 5 (2021), no. 172. https://doi.org/10.3390/fractalfract5040172.
  2. B. Benaissa, More on reverses of Minkowski's inequalities and Hardy's integral inequalities, Asian-Eur. J. Math. 13 (2020), no. 3. https://doi.org/10.1142/S1793557120500643.
  3. B. Benaissa and A. Benguessoum, Reverses Hardy-Type Inequalities Via Jensen Integral Inequality, Math. Montisnigri. 52 (2021), no. 5. https://10.20948/mathmontis-2021-52-5.
  4. B. Benaissa, Some Inequalities on Time Scales Similar to Reverse Hardy's Inequality, Rad. Hrvat. Akad. Znan. Umjet. Mat. Znan. (2022), Forthcoming papers (with pdf preview).
  5. B. Benaissa, On the Reverse Minkowski's Integral Inequality, Kragujevac. J. Math. 46 (2022), no. 3, 407-416. https://doi.org/10.46793/KgJMat2203.407B
  6. Zoubir Dahmani, Amina Khameli, and Karima Freha, Further generalizations on some hardy type RL-integral inequalities, Interdiscip. Math. J. 23 (2010), no. 8, 1487-1495. https://10.1080/09720502.2020.1754543.
  7. M. Z. Sarikaya and A. Karaca, On the k -Riemann-Liouvillefractional integral and applications, Int. J. Stat. Math. 1 (2014), no. 2, 033-043.
  8. M. Z. Sarikaya, C. C. Bilisik, and T. Tunc, On Hardy type inequalities via k-fractional integrals, TWMS J. App. Eng. Math. 10 (2020), no. 2, 443-451.
  9. Banyat Sroysang, A Generalization of Some Integral Inequalities Similar to Hardy's Inequality, Mathematica Aeterna. 3 (2013), no. 7, 593-596.
  10. W. T. Sulaiman, Reverses of Minkowski's, Holder's, and Hardy's integral inequalities, Int. J. Mod. Math. Sci. 1 (2012), no. 1, 14 -24.