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Fractal Fract
Volume 10
Issue 1
10.3390/fractalfract10010062
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Article

New Fractional Hermite–Hadamard-Type Inequalities for Caputo Derivative and MET-(p,s)-Convex Functions with Applications

by
Muhammad Sajid Zahoor
1,
Amjad Hussain
1 and
Yuanheng Wang
2,*
1
Department of Mathematics, Quaid-Azam University, Islamabad 45320, Pakistan
2
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
*
Author to whom correspondence should be addressed.
Fractal Fract. 2026, 10(1), 62; https://doi.org/10.3390/fractalfract10010062
Submission received: 10 December 2025 / Revised: 6 January 2026 / Accepted: 8 January 2026 / Published: 15 January 2026
(This article belongs to the Special Issue Advances in Fractional Integral Inequalities: Theory and Applications)
Versions Notes

Abstract

This article investigates fractional Hermite–Hadamard integral inequalities through the framework of Caputo fractional derivatives and MET-(p,s)-convex functions. In particular, we introduce new modifications to two classical fractional extensions of Hermite–Hadamard-type inequalities, formulated for both MET-(p,s)-convex functions and logarithmic (p,s)-convex functions. Moreover, we obtain enhancements of inequalities like the Hermite–Hadamard, midpoint, and Fejér types for two extended convex functions by employing the Caputo fractional derivative. The research presents a numerical example with graphical representations to confirm the correctness of the obtained results.
Keywords: fractional integral inequalities; Caputo fractional derivatives; MET-(p,s) convex functions; log (p,s) convex functions; Hermite–Hadamard inequalities. fractional integral inequalities; Caputo fractional derivatives; MET-(p,s) convex functions; log (p,s) convex functions; Hermite–Hadamard inequalities.

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MDPI and ACS Style

Zahoor, M.S.; Hussain, A.; Wang, Y. New Fractional Hermite–Hadamard-Type Inequalities for Caputo Derivative and MET-(p,s)-Convex Functions with Applications. Fractal Fract. 2026, 10, 62. https://doi.org/10.3390/fractalfract10010062

AMA Style

Zahoor MS, Hussain A, Wang Y. New Fractional Hermite–Hadamard-Type Inequalities for Caputo Derivative and MET-(p,s)-Convex Functions with Applications. Fractal and Fractional. 2026; 10(1):62. https://doi.org/10.3390/fractalfract10010062

Chicago/Turabian Style

Zahoor, Muhammad Sajid, Amjad Hussain, and Yuanheng Wang. 2026. "New Fractional Hermite–Hadamard-Type Inequalities for Caputo Derivative and MET-(p,s)-Convex Functions with Applications" Fractal and Fractional 10, no. 1: 62. https://doi.org/10.3390/fractalfract10010062

APA Style

Zahoor, M. S., Hussain, A., & Wang, Y. (2026). New Fractional Hermite–Hadamard-Type Inequalities for Caputo Derivative and MET-(p,s)-Convex Functions with Applications. Fractal and Fractional, 10(1), 62. https://doi.org/10.3390/fractalfract10010062

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