This research is concerned to some modernistic wave solutions of truncated M-fractional new Hamiltonian amplitude (NHA) equation. The dealing model relates with some disabilities of wave-train. The collected solutions can be executed in exposing of this model in prominent form. The obtained results include the trigonometric, hyperbolic trigonometric and exponential functions. Verification of the results is also done by using Mathematica tool. Two techniques named modified simplest equation (MSE) and Sardar sub-equation (SSE) techniques are employed to protect the results. The achieved results are also illustrated by 3D plots for different values of truncated M-fractional parameters. The achieved results are newer than the present results of the model in the literature. The gained results can also be fruitful for the development of model in future.