Invariant analysis, approximate solutions, and conservation laws for the time fractional higher order Boussinesq–Burgers system

• Published in: Mathematical methods in the applied sciences Vol. 47; no. 11; pp. 9137 - 9156
• Main Authors: Rahioui, Mohamed, El Kinani, El Hassan, Ouhadan, Abdelaziz
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 30.07.2024
• Subjects: approximate solutions; Boussinesq equations; Conservation laws; fractional conservation laws; Graphical representations; Invariants; Lie group analysis; Lie groups; Power series; Shallow water; time fractional higher order nonlinear B‐B system; Water waves
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.10063

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.