Conservation laws, analytical solutions and stability analysis for the time-fractional Schamel–Zakharov–Kuznetsov–Burgers equation

Abstract

Abstract In this paper, we consider the (3+1) $(3+1)$-dimensional time-fractional Schamel–Zakharov–Kuznetsov–Burgers (SZKB) equation. With the help of the Riemann–Liouville derivatives, the Lie point symmetries of the (3+1) $(3+1)$-dimensional time-fractional SZKB equation are derived. By applying the Lie point symmetry method as well as Erdélyi–Kober fractional operator, we get the similarity reductions of the time-fractional SZKB equation. Conservation laws of the time-fractional SZKB are constructed. Moreover, we obtain its power series solutions with the convergence analysis. In addition, the analytical solution is obtained by modified trial equation method. Finally, stability is analyzed graphically in different planes.

Keywords

• Lie point symmetries
• Conservation laws
• Time-fractional Schamel–Zakharov–Kuznetsov–Burgers equation
• Riemann–Liouville derivatives
• Similarity reduction
• Explicit power series