This paper investigates weighted Milne-type (M−t) inequalities within the context of Riemann–Liouville (R−L) fractional integrals. We establish multiple versions of these inequalities, applicable to different function categories, such as convex functions with differentiability properties, bounded functions, functions satisfying Lipschitz conditions, and those exhibiting bounded variation behavior. In particular, we present integral equalities that are essential to establish the main results, using non-negative weighted functions. The findings contribute to the extension of existing inequalities in the literature and provide a deeper understanding of their applications in fractional calculus. This work highlights the advantage of the established inequalities in extending classical results by accommodating a broader class of functions and yielding sharper bounds. It also explores potential directions for future research inspired by these findings.
Almoneef et al. (2025) studied this question.