In this research, three different time-varying mean-variance portfolio optimization (MVPO) problems are addressed using the zeroing neural network (ZNN) approach. The first two MVPO problems are defined as time-varying quadratic programming (TVQP) problems, while the third MVPO problem is defined as a time-varying nonlinear programming (TVNLP) problem. Then, utilizing real-world datasets, the time-varying MVPO problems are addressed by this alternative neural network (NN) solver and conventional MATLAB solvers, and their performances are compared in three various portfolio configurations. The results of the experiments show that the ZNN approach is a magnificent alternative to the conventional methods. To publicize and explore the findings of this study, a MATLAB repository has been established and is freely available on GitHub for any user who is interested.