Time fractional super KdV equation: Lie point symmetries, conservation laws, explicit solutions with convergence analysis

Abstract

In this work, one-point Lie symmetry method is applied to time fractional super KdV equation in order to obtain similarity variables and similarity transformations with Riemann–Liouville derivative. These transformations reduce the governing equation to an ordinary differential equation of fractional order. A new and effective conservation theorem based on Noether’s theorem is used to obtain conserved vectors. Then, we construct power series solutions for the reduced time fractional ordinary differential equation and prove that the solutions are convergent. Lastly, some interesting graphs are given to explain physical behaviors.

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

“…By using the power series method [19,20,39,40], we intend to construct analytic approximate solutions of the time fractional higher order B-B system.…”

Application of Jordan canonical form and symplectic matrix in fractional differential models

“…Fractional calculus has played an irreplaceable role in many fields and attracted more and more attention [1][2][3][4][5][6][7][8][9][10][11][12][13]. In this paper, we mainly have two contributions.…”