Fractional Refinements of Hermite-Hadamard Type Inequality Involving Mittag-Leffler and Raina's Mappings with Applications to Special Means

Fractional integrals have lately become prominent in inequality analysis and have been the focus of several investigations. A new trend in inequality theory has emerged as a result of the investigation of various types of inequality. We use the ψ-Riemann Liouville k-fractional integral operator to derive a new Hermite-Hadamard type inequality. Additionally, two fractional lemmas are derived. The ψ-Riemann Liouville k-fractional operator is used to generate several Hermite-Hadamard type modifications that result in these lemmas. The recently introduced Hermite-Hadamard type inequality has been used to obtain applications to means. A comprehensive reference study is provided to assist readers in navigating this quickly evolving topic, given the growing significance of Mittag-Leffler and Raina-type functions.