  As we are aware, various types of methods have been proposed to approximate
the Caputo fractional derivative numerically. A common challenge of the methods
is the non-local property of the Caputo fractional derivative which leads to
the slow and memory consuming methods. Diffusive representation of fractional
derivative is an efficient tool to overcome the mentioned challenge. This paper
presents two new diffusive representations to approximate the Caputo fractional
derivative of order $0<\alpha<1$. Error analysis of the newly presented methods
together with some numerical examples are provided at the end.
