<p>In this work, we investigated approximative solutions to time-fractional modified Korteweg–de Vries equations of seventh order including Lax, Kaup–Kuperschmidt, and Sawada Kotera Ito equations using the Shehu Adomian decomposition method. These equations arise in fluid mechanics, nonlinear optics, ocean dynamics, and capillary gravity modelling to represent the propagation of long waves occurring in shallow water. We employed Caputo, Caputo–Fabrizio, and Atangana–Baleanu in the Caputo sense fractional differential operators to the proposed method. To validate the current technique, we considered three different cases of time-fractional modified Korteweg–de Vries equations, and the obtained results were compared to the solution of other available approaches. The numerical findings are coherent with previous findings. It can be seen in the graphical simulations that the solutions yield soliton wave phenomena. In the current investigation, convergence analysis and uniqueness are also mentioned.</p>