SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 71 Issue: 3

The Minkowski type inequalities for weighted fractional operators

Çetin Yıldız(ATATURK UNIVERSITY)0000-0002-8302-343X
Mustafa Gürbüz(AGRI IBRAHIM CECEN UNIVERSITY)0000-0002-7092-4298
Pages
—
Publication Date
2022-09-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In addition, new fractional integral inequalities related to Minkowski type are also established.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this article, inequalities of reverse Minkowski type involving weighted fractional operators are investigated.
📊
Key Findings & Data:In this article, inequalities of reverse Minkowski type involving weighted fractional operators are investigated.
💡
Conclusion & Impact:In addition, new fractional integral inequalities related to Minkowski type are also established.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Weighted fractional operators · fractional integral inequality · Minkowski inequality

Abstract

In this article, inequalities of reverse Minkowski type involving weighted fractional operators are investigated. In addition, new fractional integral inequalities related to Minkowski type are also established.

🔖

Cite This Article

Yıldız, Ç., Gürbüz, M. (2022). The Minkowski type inequalities for weighted fractional operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 71 Issue: 3. https://doi.org/10.31801/cfsuasmas.1054069

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (32)

  1. Abdeljawad, T., On conformable fractional calculus, J. Comput. Appl. Math, 279 (2015), 57–66. https://doi.org/10.1016/j.cam.2014.10.016
  2. Akdemir, A.O., Butt, S.I., Nadeem, M., Ragusa, M.A., New general variants of Chebyshev type inequalities via generalized fractional integral operators, Mathematics, 9(2) (2021), 122. https://doi.org/10.3390/math9020122
  3. Bayraktar, B., Some integral inequalities of Hermite-Hadamard type for differentiable (s,m)-convex functions via fractional integrals, TWMS Jour. App. Engin. Math., 10(3) (2020), 625-637.
  4. Belarbi, S., Dahmani, Z., On some new fractional integral inequalities, J. Ineq. Pure and Appl. Math., 10(3) (2009), art. 86.
  5. Bougoffa, L., On Minkowski and Hardy integral inequalities, J. Ineq. Pure & Appl. Math., 7(2) (2006), art. 60.
  6. Butt, S.I., Nadeem, M., Farid, G., On Caputo fractional derivatives via exponential s-convex functions, Turkish Jour. Sci., 5(2) (2020), 140-146.
  7. Butt, S.I., Umar, M., Rashid, S., Akdemir, A.O., Chu, Y.M., New Hermite-Jensen-Mercer-type inequalities via k-fractional integrals, Adv. Diff. Equat., 1 (2020), 1-24. https://doi.org/10.1186/s13662-020-03093-y
  8. Chinchane, V.L., Pachpatte, D.B., New fractional inequalities via Hadamard fractional integral, Int. J. Funct. Anal., 5 (2013), 165-176.
  9. Dahmani, Z., On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1(1) (2010), 51–58. https://doi.org/10.15352/afa/1399900993
  10. Ekinci, A., Özdemir, M.E., Some new integral inequalities via Riemann-Liouville integral operators, App. Comp. Math., 3(18) (2019), 288–295.
  11. Ekinci, A., Özdemir, M.E., Set, E., New integral inequalities of Ostrowski type for quasi−convex functions with applications, Turkish Jour. Sci., 5(3) (2020), 290-304.
  12. Hardy, G.H., Littewood, J.E., P`olya, G., Inequalities, 2nd ed. Cambridge, England: Cambridge University Press, 1988, pp.30-32, 123, 146-150.
  13. Jarad, F., Abdeljawad, T., Shah, K., On the weighted fractional operators of a function with respect to another function, Fractals, 28(08) (2020), 2040011. https://doi.org/10.1142/S0218348X20400113
  14. Jarad, F., Ugurlu, U., Abdeljawad, T., Baleanu, D., On a new class of fractional operators, Adv. Differ. Equ, 2017(247) (2017), 1-16. https://doi.org/10.1186/s13662-017-1306-z
  15. Katugampola, U.N., New approach to generalized fractional integral, Appl. Math. Comput., 218 (2011), 860-865. https://doi.org/10.3390/math10040573
  16. Katugampola, U.N., A new approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6 (2014), 1-15.
  17. Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65–70. https://doi.org/10.1016/j.cam.2014.01.002
  18. Khan, T.U., Khan, M.A., Generalized conformable fractional integral operators, J. Comput. Appl. Math., 346 (2019), 378–389. https://doi.org/10.1016/j.cam.2018.07.018
  19. Kızıl, S¸., Ardı¸c, M.A., Inequalities for strongly convex functions via Atangana-Baleanu integral operators, Turkish Jour. Sci., 6(2) (2021), 96-109.
  20. Liouville, J., Memoire sur quelques questions de geometrie et de mecanique, et sur un nouveau genre de calcul pour resoudre ces questions, Journal de l’ Ecole Polytechnique, 13 (1832), 1–69.
  21. Miller, K.S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
  22. Mitrinovic, D.S., Peˇcari´c, J.E., Fink, A.M., Classical and New Inequalities in Analysis, Kluwer Academic Publishers, London, 1993.
  23. Mohammed, P.O., Abdeljawad, T., Alqudah, M.A., Jarad, F., New discrete inequalities of Hermite–Hadamard type for convex functions, Adv. Diff. Equat., 1 (2021), 1-10. https://doi.org/10.1186/s13662-021-03290-3
  24. Mohammed, P.O., Abdeljawad, T., Kashuri, A., Fractional Hermite-Hadamard-Fejer inequalities for a convex function with respect to an increasing function involving a positive weighted symmetric function, Symmetry, 12(9) (2020), 1503. https://doi.org/10.3390/sym12091503
  25. Mohammed, P.O., Abdeljawad, T., Zeng, S., Kashuri, A., Fractional Hermite-Hadamard integral inequalities for a new class of convex functions, Symmetry, 12(9) (2020), 1485. https://doi.org/10.3390/sym12091485
  26. Özdemir, M.E., Dragomir, S.S., Yıldız, Ç., The Hadamard inequality for convex function via fractional integrals, Acta Math. Sci., 33B(5) (2013), 1293-1299. https://doi.org/10.1016/S0252-9602(13)60081-8
  27. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.
  28. Sarıkaya, M.Z., Yaldız, H., On generalization integral inequalities for fractional inegrals, Nihonkai Math. J., 25 (2014), 93-104.
  29. Set, E., Akdemir, A.O., Gözpınar, A., Jarad, F., Ostrowski type inequalities via new fractional conformable integrals, AIMS Mathematics, 4(6) (2019), 1684–1697. https://doi.org/10.3934/math.2019.6.1684
  30. Set, E., Özdemir, M.E., Dragomir, S.S., On the Hermite–Hadamard inequality and other integral inequalities involving two functions, J. Ineq. Appl., 2010(148102) (2010), 1-9. https://doi.org/10.1155/2010/148102
  31. Sousa, J.V.D.C., de Oliveira, E.C., The Minkowski’s inequality by means of a generalized fractional integral, AIMS Mathematics, 3(1) (2018), 131-142. https://doi.org/10.3934/Math.2018.1.131
  32. Yavuz, M., Özdemir, N., Comparing the new fractional derivative operators involving exponential and Mittag-Leffler kernel, Discrete Contin. Dyn. Syst., Ser., 13(3) (2020), 995. https://doi.org/10.3934/dcdss.2020058