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Fractional Hermite-Hadamard inequalities containing generalized Mittag-Leffler function.

Marcela V Mihai¹, Muhammad Uzair Awan², Muhammad Aslam Noor³

¹Department Scientific-Methodical Sessions, Romanian Mathematical Society-branch Bucharest, Academy Street no. 14, Bucharest, RO-010014 Romania.

Journal of Inequalities and Applications

|November 7, 2017

Summary

This study refines fractional Hermite-Hadamard inequalities using harmonically convex functions. New results incorporate the generalized Mittag-Leffler function for enhanced mathematical analysis.

Keywords:

Hermite-Hadamard inequalities Mittag-Leffler function harmonic convex function

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Area of Science:

Mathematical Analysis
Fractional Calculus
Convexity Theory

Background:

The Hermite-Hadamard inequalities are fundamental in convex analysis.
Fractional calculus extends classical calculus concepts to non-integer orders.
Harmonically convex functions represent a specific class of convex functions with unique properties.

Purpose of the Study:

To establish novel refinements of the fractional Hermite-Hadamard inequalities.
To utilize harmonically convex functions within the framework of fractional calculus.
To incorporate the generalized Mittag-Leffler function as a kernel in these inequalities.

Main Methods:

Application of fractional integral operators.
Properties of harmonically convex functions.
Techniques for refining integral inequalities.
Utilizing the generalized Mittag-Leffler function kernel.

Main Results:

New refined fractional Hermite-Hadamard inequalities are derived.
The results are specialized for harmonically convex functions.
The generalized Mittag-Leffler function plays a key role in the refined inequalities.

Conclusions:

The established inequalities offer significant advancements in fractional integral inequality theory.
These findings contribute to a deeper understanding of Hermite-Hadamard inequalities in the context of fractional calculus.
The use of the generalized Mittag-Leffler function provides a more generalized framework for such inequalities.