Enhancing Some Inequalities via Fractional Extended Riemann–Liouville Integrals: Jensen–Mercer Perspective

ABSTRACT This paper aims to derive novel forms of trapezoid and midpoint inequalities within the context of fractional extended Riemann–Liouville integrals (FERLIs). The approach relies on the foundational Jensen–Mercer inequality to develop the arguments. Central to the development are several identities involving FERLIs and ‐convex functions that form the basis of the obtained results. Relationships with earlier studies concerning both classical and extended Riemann–Liouville fractional integrals are examined.