In this paper, we consider the existence of normalized solutions for the fractional Kirchhoff system with Hardy critical nonlinearities. The problem combines the challenges of nonlocal operators, singular critical effects, and a variational framework with fixed mass conditions. By employing the minimax theorem, analyzing the Palais–Smale sequence and restricting to radial functions, we overcome the loss of strong convergence at critical energy levels. Under L2-supercritical case, we prove the existence of positive radial normalized solutions, along with the positivity of the corresponding Lagrange multipliers.
Wang et al. (Fri,) studied this question.