Extending the Scope of the Fractional Hardy Integral Inequality

In this article, we establish two theorems that generalize the fractional Hardy integral inequality by incorporating several intermediate functions and parameters. The assumptions made are tractable. Some of them can be related to the notions of sub-additivity and sub-multiplicativity. The proofs are self-contained, without intermediate results, and all details are given. We thus extend the applicability of a classical integral inequality and offer new potential applications in mathematical analysis.