Approximate solution of initial boundary value problems for ordinary differential equations with fractal derivative

Abstract

Fractal ordinary differential equations are successfully established by He's fractal derivative in a fractal space, and their variational principles are obtained by semi-inverse transform method.Taylor series method is used to solve the given fractal equations with initial boundary value conditions, and sometimes Ying Buzu algorithm play an important role in this process. Examples show the Taylor series method and Ying Buzu algorithm are powerful and simple tools.