Refined fractional Ostrowski–Mercer-type inequalities for s-convex functions and their applications

Convexity and fractional integral operators play an important role in many areas of mathematical analysis. In this work, we first derive a new identity related to fractional Ostrowski–Mercer-type inequalities. By employing this identity together with Young’s inequality, Hölder’s inequality, and the power-mean inequality, several new extensions of Ostrowski–Mercer-type inequalities are established for s -convex functions. Some interesting special cases are also obtained from the main results. Furthermore, applications involving the midpoint formula, the modified Bessel function, and the q -digamma function are presented. Graphical illustrations are provided to support the analytical results.