Shifted Vieta-Fibonacci polynomials for the fractal-fractional fifth-order KdV equation

In this article, the fractal-fractional (FF) version of the fifth-order KdV equation is introduced. The shifted Vieta-Fibonacci (VF) polynomials are generated and adopted to establish a simple and accurate numerical method for solving this equation. To this end, the operational matrices of ordinary and FF derivatives of these polynomials are obtained in explicit forms. These matrices together with the series expansion of the shifted VF polynomials are mutually utilized to convert the original equation into a system of algebraic equations which is much easier. Some numerical examples are examined to show the power and accuracy of the method.