Weighted multiplicative fractional integrals: Analytical properties and applications in Weddle's rule error estimation

This paper investigates the weighted multiplicative fractional integral operators. We introduce these operators and study their properties, including [Formula: see text]integrability, [Formula: see text]continuity, commutativity, boundedness, and semigroup property. By establishing a weighted fractional Weddle-type identity, we derive corresponding inequalities under two convexity conditions: (i) multiplicative convexity of [Formula: see text], and (ii) convexity of [Formula: see text] for [Formula: see text]. Numerical examples and graphical illustrations validate our results.