SITEM for the conformable space-time fractional Boussinesq and (2 + 1)-dimensional breaking soliton equations

•The new traveling wave solutions for the space-time fractional Boussinesq and (2 + 1)-dimensional breaking soliton equations are obtained.•Fractional derivatives are defined by conformable sense.•The obtained traveling wave solutions are expressed by the hyperbolic, trigonometric, exponential and rational functions.•Simulations of the obtained traveling solutions are given. In the present paper, new analytical solutions for the space-time fractional Boussinesq and (2 + 1)-dimensional breaking soliton equations are obtained by using the simplified tan(ϕ(ξ)2)-expansion method. Here, fractional derivatives are defined in the conformable sense. To show the correctness of the obtained traveling wave solutions, residual error function is defined. It is observed that the new solutions are very close to the exact solutions. The solutions obtained by the presented method have not been reported in former literature.