Generalized Fractional Integral Extensions of Hermite-Hadamard Inequalities via Extended Mittag-Leffler Kernel (European Journal of Pure and Applied Mathematics, 2025)
In this article, we provid a number of Hermite-Hadamard type fractional integral inequalities for the Atangana-Baleanu and Prabhakar fractional operators, using extended generalized Mittag-Leffler functions as their kernel. Significant findings are provided for the integral inequalities involving fractional integrals of the type $({{\Im_1}}+, {{\Im_2}}-)$ and $(\frac{{{\Im_1}} + {{\Im_2}}}{2})$. By employing certain functions to create visual graphs with matching numerical entries that depict the inequalities, we show the veracity of our findings.
Keywords: Atangana-Baleanu fractional calculus; Fractional calculus; Hermite-Hadamard inequality; Generalized fractional integral operators; Mittag-Leffler function