Time Fractional Zakharov-Kuznetsov Research Articles

Approximate analytical solution to a time-fractional Zakharov-Kuznetsov equation

In this paper we present the approximate analytical solution of a time-fractional Zakharov-Kuznetsov equation via the fractional iteration method. The fractional derivatives are described in the Caputo sense. The approximate results show that the fractional iteration method is a very ecient technique to handle fractional partial differential equations.

NUMERICAL ANALYSIS OF AN IMPLICIT FULLY DISCRETE LOCAL DISCONTINUOUS GALERKIN METHOD FOR THE FRACTIONAL ZAKHAROV–KUZNETSOV EQUATION

In this paper we develop and analyze an implicit fully discrete local discontinuous Galerkin (LDG) finite element method for a time-fractional Zakharov–Kuznetsov equation. The method is based on a finite difference scheme in time and local discontinuous Galerkin methods in space. We show that our scheme is unconditional stable and L 2 error estimate for the linear case with the convergence rate through analysis.