Novel Extensions of Hermite-Hadamard Type Inequalities via the Riemann-Liouville Fractional Integral Operator

Abstract

This study establishes novel Hermite-Hadamard type inequalities involving the Riemann-Liouville fractional integral operator under the condition that the absolute value of the derivative is convex. By applying the characteristics of convex functions for fractional integral inequalities, we establish improved integral bounds that enhance and extend existing results in the literature. Furthermore, our findings offer new insights into the relationship between convexity and new fractional integral operators, which generalize the recent developments. We also present several mathematical models to validate our findings. Overall, the article provides an interesting set of fractional integral inequalities that are ideal for advanced instruction and future research.