Invariant analysis, approximate solutions, and conservation laws for the time fractional higher order Boussinesq–Burgers system
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 st...
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Published in | Mathematical methods in the applied sciences Vol. 47; no. 11; pp. 9137 - 9156 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Freiburg
Wiley Subscription Services, Inc
30.07.2024
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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Bibliography: | Funding information There are no funders to report for this submission. |
ISSN: | 0170-4214 1099-1476 |
DOI: | 10.1002/mma.10063 |