Solving the Nonlinear Time-Fractional Zakharov-Kuznetsov Equation with the Chebyshev Spectral Method

Abstract

In this study, we introduce a new application to a spectral approach for solving two-dimensional (2D) time-fractional Zakhrov-Kuznetsov equations (TFZKEs) with initial conditions (ICs) and boundary conditions (BCs). When the regular magnetic domain is present, this equation represents a model that illustrates the conduct of weakly nonlinear ionic phonetic waves in a plasma that provides cool ions and an electronically isothermal environment. The fundamental qualifiers of fractional derivatives are characterized in the Caputo concept. We propose a new numerical approach that relies on shifted Chebyshev polynomials (SCPs) as test functions and uniformly grid points for time and space. In the field of fractional calculus, we have to introduce several schemes to evaluate a solution to the nonlinear fractional problems. This new technique is a preferable attempt. The results show that the current method is quite effective, and robust which provides excellent accuracy, and is appropriate for implementation to solve many significant fractional differential equations.