Fractional Integral Inequalities Involving Harmonic Convexity with Exponential Kernels and Applications

Abstract

In this article, we establish several new and improved variants of Hermite--Hadamard and Pachpatte type integral inequalities by employing a generalized fractional operator with an exponential kernel for mappings of harmonic Godunova--Levin type. In addition, we investigate a sandwich-type theorem and the Hyers--Ulam stability for this class of generalized convex functions. To demonstrate the effectiveness and sharpness of the obtained inequalities, we construct non-trivial examples and provide graphical illustrations, together with tabulated numerical values of the fractional operator for various choices of the fractional parameters $\alpha$ and $\beta$ in the interval $(0,1)$. Finally, we apply our main results to derive error estimates for the trapezoidal numerical integration rule.

Keywords

• Trapezoidal rule
• Hermite--Hadamard inequality
• Harmonically $\mathrm{h}$-Godunova--Levin function
• Exponential kernels
• Hyers--Ulam stability

References

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