Some Results Within the Framework of Conformable Fractional Calculus

Authors

  • Muhammad Tariq Department of Mathematics, Balochistan Residential College, Loralai, Balochistan, Pakistan
  • Tonguc Cagin College of Business Administration, American University of the Middle East, Kuwait
  • Huseyin Budak Department of Mathematics, Faculty of Science and Arts, Kocaeli University, Kocaeli, Türkiye
  • Clemente Cesarano Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma , Itlay
  • Maggie Aphane National Institute for Theoretical and Computational Sciences (NITheCS)................. Sefako Makgatho Health Sciences University, Garankuwa, Medusa, 0204, South Africa

Keywords:

Conformable fractional integral; harmonic h-Godunova–Levin functions; Pachpattetype inequalities

Abstract

In this paper, we employ fractional conformable integral operators to develop novel versions of Pachpatte-type integral inequalities for functions defined on harmonic sets, namely for harmonic h-Godunova–Levin mappings. We provide nontrivial numerical examples accompanied by graphical illustrations for different values of the fractional parameters to show the validity and application of the derived results.

References

[1] Pachpatte, B.G. On some inequalities for convex functions. RGMIA Research Report Collection. 6 (2003), 1–8.

[2] Ahmad, B.; Alsaedi, A.; Kirane, M.; Torebek, B.T. Hermite–Hadamard, Hermite–Hadamard–Fejér, Dragomir–Agarwal and Pachpatte type inequalities for convex functions via new fractional integrals. J. Comput. Appl. Math. 2019, 353, 120–129.

[3] M. Tariq, A. A. Shaikh, and S. K. Ntouyas, A comprehensive review of the Pachpatte-type inequality pertaining to fractional integral operators, Surv. Math. Appl., 20 (2025), 25–74.

[4] M. Tariq.; S.K. Ntouyas.; J. Tariboon. Some new variants of fractional Hermite-Hadamard and Pachpatte-type integral inequalities involving Raina’s and Mittag-Leffer functions with

applications, Journal of Mathematics and Computer Science, 40, 2025, 415-443.

[5] ˙I¸scan, ˙I. Hermite-Hadamard type inequalities for harmonically convex functions. Hacettepe J. Math. Stat. 2014, 43, 935–942.

[6] Afzal, W.; Shabbir, K.; Trean¸ta, S.; Nonlaopon, K. Jensen and Hermite-Hadamard type ˘ inclusions for harmonical h-Godunova-Levin functions. AIMS Math. 2023, 8, 3303–3321.

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Published

30-06-2026

Issue

Vol. 1 No. 01 (2026): June 2026

Section

Articles

License

Copyright (c) 2026 Muhammad Tariq, Tonguc Cagin, Huseyin Budak, Clemente Cesarano, Maggie Aphane (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

https://creativecommons.org/licenses/by/4.0

How to Cite

Some Results Within the Framework of Conformable Fractional Calculus. (2026). International Journal of Applied Mathematics , Optimization and Artificial Intelligence, 1(01), 21-30. https://ijamoai.org/ijamoai/index.php/ojs/article/view/14