We implement the fractional Hirota bilinear technique to compute analytical solution for hyperbolic generalized space–time fractional Burgers model. We construct double soliton wave for the desired fractional differential model under study. These calculations are performed by the symbolic computation such as maple, which has been used more recently by researchers which proves that the Hirota bilinear method is a promising and straightforward procedure for treatment nonlinear differential models of integer and fractional orders. We checked whether the results demonstrate that the process is easy to calculate, effective, and direct to address a wide range of engineering and physics models. The arbitrary and random selection of the fractional orders enables us and allow to build richer structures. The changes in the soliton based on the changes of fractional order allows more applications in applied sciences. The dynamical behavior of the obtained solutions have been depicted and underlined in 3D and 2D graphical drawings with different chooses of the fractional order.