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In this paper, we investigate the Lie group formalism for the time fractional generalized nonlinear Broer–Kaup system in the sense of Riemann–Liouville fractional partial derivative. The Lie algebra corresponding to the symmetry groups in which the studied equation remains invariant is established, and the similarity reductions are performed. Next, based on the invariant subspace method as well as the power series method, including the convergence analysis, some exact solutions of the time fractional generalized Broer–Kaup system and its standard form are derived. Moreover, in order to show the dynamical behavior and the impact of the fractional order on the profile of solutions, some figures in 2D and 3D have been depicted. Finally, in accordance with the nonlinear self-adjointness property, conservation laws are successfully formulated using infinitesimal symmetries. [ABSTRACT FROM AUTHOR]

In this paper, the Lie symmetry group method is employed to study the time fractional generalized advection–diffusion equation. The Lie symmetry algebra classification is established by considering three different cases. Next, the similarity reductions are performed, and some solutions including invariants are derived. Finally, conservation laws are successfully constructed using the symmetry generators. [ABSTRACT FROM AUTHOR]