Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina's Mappings with Applications to Special Means

Hijaz Ahmad; Muhammad Tariq; Waqar Afzal; Mustafa Bayram; Evren Hincal

doi:10.32323/ujma.1925583

Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina's Mappings with Applications to Special Means

Abstract

Fractional integrals have lately become prominent in inequality analysis and have been the focus of several investigations. A new trend in inequality theory has emerged as a result of the investigation of various types of inequality. We use the $\psi$-Riemann Liouville $k$-fractional integral operator to derive a new Hermite-Hadamard type inequality. Additionally, two fractional lemmas are derived. The $\psi$-Riemann Liouville $k$-fractional operator is used to generate several Hermite-Hadamard type modifications that result in these lemmas. The recently introduced Hermite-Hadamard type inequality has been used to obtain applications to means. A comprehensive reference study is provided to assist readers in navigating this quickly evolving topic, given the growing significance of Mittag-Leffler and Raina-type functions.

Keywords

Convex functions, Hermite-Hadamard inequality, $\psi$-Riemann-Liouville, $k$-fractional integral operators

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Hijaz Ahmad
0000-0002-5438-5407
Kuzey Kıbrıs Türk Cumhuriyeti

Muhammad Tariq ^*
0000-0001-8372-2532
Kuzey Kıbrıs Türk Cumhuriyeti

Waqar Afzal
0000-0001-7879-1920
Pakistan

Mustafa Bayram
0000-0002-2994-7201
Türkiye

Evren Hincal
0000-0001-6175-1455
Kuzey Kıbrıs Türk Cumhuriyeti

Early Pub Date

August 31, 2026

Publication Date

-

Submission Date

April 8, 2026

Acceptance Date

August 29, 2026

Published in Issue

Year 2026 Number: Advanced Online Publication

DOI

https://doi.org/10.32323/ujma.1925583

IZ

https://izlik.org/JA39DP38YH

APA

Ahmad, H., Tariq, M., Afzal, W., Bayram, M., & Hincal, E. (2026). Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina’s Mappings with Applications to Special Means. Universal Journal of Mathematics and Applications, Advanced Online Publication. https://doi.org/10.32323/ujma.1925583

AMA

1.Ahmad H, Tariq M, Afzal W, Bayram M, Hincal E. Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina’s Mappings with Applications to Special Means. Univ. J. Math. Appl. 2026;(Advanced Online Publication). doi:10.32323/ujma.1925583

Chicago

Ahmad, Hijaz, Muhammad Tariq, Waqar Afzal, Mustafa Bayram, and Evren Hincal. 2026. “Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina’s Mappings With Applications to Special Means”. Universal Journal of Mathematics and Applications, no. Advanced Online Publication. https://doi.org/10.32323/ujma.1925583.

EndNote

Ahmad H, Tariq M, Afzal W, Bayram M, Hincal E (August 1, 2026) Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina’s Mappings with Applications to Special Means. Universal Journal of Mathematics and Applications Advanced Online Publication

IEEE

[1]H. Ahmad, M. Tariq, W. Afzal, M. Bayram, and E. Hincal, “Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina’s Mappings with Applications to Special Means”, Univ. J. Math. Appl., no. Advanced Online Publication, Aug. 2026, doi: 10.32323/ujma.1925583.

ISNAD

Ahmad, Hijaz - Tariq, Muhammad - Afzal, Waqar - Bayram, Mustafa - Hincal, Evren. “Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina’s Mappings With Applications to Special Means”. Universal Journal of Mathematics and Applications. Advanced Online Publication (August 1, 2026). https://doi.org/10.32323/ujma.1925583.

JAMA

1.Ahmad H, Tariq M, Afzal W, Bayram M, Hincal E. Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina’s Mappings with Applications to Special Means. Univ. J. Math. Appl. 2026. doi:10.32323/ujma.1925583.

MLA

Ahmad, Hijaz, et al. “Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina’s Mappings With Applications to Special Means”. Universal Journal of Mathematics and Applications, no. Advanced Online Publication, Aug. 2026, doi:10.32323/ujma.1925583.

Vancouver

1.Hijaz Ahmad, Muhammad Tariq, Waqar Afzal, Mustafa Bayram, Evren Hincal. Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina’s Mappings with Applications to Special Means. Univ. J. Math. Appl. 2026 Aug. 1;(Advanced Online Publication). doi:10.32323/ujma.1925583