<p>Integrating models and data to reconstruct solutions for transport problems involving temporal non-local operators is a complex and computationally intensive task. In this paper, we propose a stabilized back-forth nudging method to achieve efficient and stabilized integration of fractional transport models with data, thereby reconstructing high-precision solutions. First, we conduct a theoretical analysis of the reasons behind the failure of the back-forth nudging method for fractional models, redesign the back-forth nudging method specifically for fractional transport equations, and provide sufficient conditions for the stability and convergence of the algorithm. Stabilized finite difference schemes are developed for both forward and backward evolutionary equations, leading to the construction of stabilized back-forth nudging method. Sufficient convergence conditions are established for the discrete back-forth nudging schemes, accompanied by unified parameter configuration criteria established for fractional transport equation with full or sparse observation. Numerical experiments support our theoretical findings, demonstrating the reliability and efficiency of the proposed algorithm.</p>