The present work offers a new model of (1+n)-dimensional fractional Burgers' equation ((1+n)D-FBE) and presents a comparative numerical study of three efficient semi analytical techniques for solving the ((1+n)D-FBEs). These techniques include the Laplace Adomian decomposition method (LADM), the Laplace variational iteration method (LVIM) and the reduced differential transform method (RDTM). The suggested approaches consider the use of the suitable initial conditions and find the solutions without any discretization, transformation or limiting traditions. Furthermore, their solutions are in the form of quickly convergent series with easily calculable terms. Numerical studies of four numerical applications are provided to certify the effectiveness and reliability of the suggested approaches, also to compare their computational effectiveness with each other and with other supplementary methods in the available literature. In addition to explore the properties of the solutions when changing the fractional derivative parameter. Numerical results demonstrate the effectiveness and accuracy of the suggested methods.