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 are 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.