<p>In this paper, we study an inverse problem aimed at reconstructing the initial data for time- and space-fractional, nonscalar, coupled parabolic systems. Using spectral analysis, we establish the identifiability of the problem by proving the existence and uniqueness of the initial condition corresponding to the given final observed data. Furthermore, we show that the inverse problem is ill-posed. To address this issue, we formulate the problem as a regularized optimization problem by minimizing a least-squares-type cost functional. Numerical simulations are provided to illustrate the effectiveness of the proposed approach and to validate the theoretical results.</p>