A numerical method for finding solution of the distributed‐order time‐fractional forced Korteweg–de Vries equation including the Caputo fractional derivative

Abstract

In this paper, for the first time, the distributed-order time-fractional forced Korteweg-de Vries equation is studied. We use a numerical method based on the shifted Legendre operational matrix of distributed-order fractional derivative with Tau method to find approximate solution of distributed-order forced Korteweg-de Vries equation. This shifted Legendre operational matrix of distributed-order fractional derivative with Tau method is used to reduce the solution of the distributed-order time-fractional forced Korteweg-de Vries equations to a system of algebraic equations. An error analysis and convergence are obtained. Finally, to display the applicability and validity of the numerical method, some examples are implemented.