New Fractional Mercer–Ostrowski Type Inequalities with Respect to Monotone Function

This research focuses on Ostrowski type inequality in the form of classical Mercer inequality via -Riemann–Liouville fractional integral (F-I) operators. Using the -Riemann–Liouville F-I operator, we first develop and demonstrate a new generalized lemma for differentiable functions. Based on this lemma, we derive some fractional Mercer–Ostrowski type inequalities by using the convexity theory. These new findings extend and recapture previous published results. Finally, we presented applications of our work via the known special functions of real numbers such as q-digamma functions and Bessel function.