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Hermite-Hadamard type inequalities for fractional integrals via Green's function
Muhammad Adil Khan1,2, Arshad Iqbal2, Muhammad Suleman2
11College of Science, Hunan City University, Yiyang, China.
Journal of Inequalities and Applications
|August 24, 2018
Summary
This study introduces new fractional Hermite-Hadamard inequalities using Green's function and Jensen's inequality. These findings extend existing inequalities for convex and monotone functions.
Area of Science:
- Mathematical Analysis
- Fractional Calculus
Background:
- The Hermite-Hadamard inequality is a fundamental result in convex analysis.
- Fractional calculus provides tools to generalize classical calculus concepts.
Purpose of the Study:
- To establish novel left Riemann-Liouville fractional Hermite-Hadamard type inequalities.
- To derive generalized Hermite-Hadamard type inequalities.
- To present new inequalities for convex and monotone functions.
Main Methods:
- Utilizing Green's function for inequality derivation.
- Applying Jensen's inequality in the fractional context.
- Developing new fractional integral inequalities.
Main Results:
- Established left Riemann-Liouville fractional Hermite-Hadamard inequalities.
- Derived generalized Hermite-Hadamard inequalities.
- Presented new inequalities for convex and monotone functions.
Conclusions:
- The study successfully extends Hermite-Hadamard inequalities into the fractional domain.
- New inequalities offer valuable tools for analyzing convex and monotone functions.