In this study we investigate soliton solutions, collision effects and breather solution for (3+1)-dimensional time-fractional Korteweg- de Vries - Zakharov - Kuznetsov (KDV-ZK)-like models. The fractional derivatives are described in terms of truncated M-fractional derivatives. Using certain permutations as well as the travelling wave method we derive one-, two- and three-soliton solutions and breather solution by Hirota method. It is noteworthy that this method has not previously been employed in the resolution of such equations. We use graphs to analyse the effect of fractional order parameters on the results. Furthermore, a discourse was had concerning the applicability and limitations of the aforementioned methods and results. It has been demonstrated that the effect of μ is confined to the amplitude of the soliton. It can thus be demonstrated that the two parameters of the truncated M-fractional order have the capacity to affect the amplitude and the width of the soliton. Moreover, the collision interaction between two solitons, and between three solitons, is elastic.
Li et al. (Sat,) studied this question.