Affiliation:
1. Department of Mathematics, Faculty of Sciences, Laboratory of Mathematics, Analysis and Control of Systems Moulay Ismail University Meknes Morocco
2. Regional Center for the Professions of Education and Training, Mathematical and Didactical Research Team Meknes Morocco
Abstract
In this paper, we employ the time fractional higher order nonlinear Boussinesq–Burgers system to investigate shallow water waves based on the Riemann–Liouville and Caputo fractional partial derivatives. The Lie algebra of infinitesimal generators associated with the symmetry groups that leave the studied system invariant is systematically constructed, and the similarity reductions are established. Furthermore, conserved quantities of the system under consideration are formulated. Next, the power series solution, including the convergence analysis, is obtained. Based on the fractional Sumudu–Adomian decomposition method, some approximate solutions are derived. Finally, in order to show the efficiency of the considered methods, the effect of the fractional order, as well as the dynamical behavior of solutions, numerical validation and graphical representations are designed.