In this paper, the time-fractional Jaulent-Miodek system associated with energy-dependent Schrodinger potential is solved by the modified Laplace decomposition method. The Caputo fractional derivative is considered throughout the paper. The attained solutions using the method are analyzed and compared with the solutions of the existing studies in the literature to demonstrate the efficacy and applicability of the technique. The results are summarized in the tables and figures. We use Mathematica for all computations and figures in the paper. The method is competitive, easily computable, and adaptable to solving various nonlinear problems.