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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.
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.
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