In this talk,we will discuss how to calculate the time-domain response of the nabla fractional order system effectively.Two kinds of methods will be mentioned,i.e.,the frequency-domain based method and the time-domain based method.For the former one,the frequency distributed model is adopted,which can be regarded as the true state space model of the nabla fractional order system.The difficulty lies in that such model isinfinite dimensional.To realize it using Matlab platform,a finite dimensional approximation scheme is proposed firstly.To accommodate different definitions,the initial condition is carefully configured.Afterwards,two simulink module-based approaches are adopted.For the latter one,by substituting the definition of nabla fractional difference,the problem can be transformed into aseries of nonlinear algebraic equations.With the help of the proven numerical calculation methods,our problem can be solved indirectly.Finally,a series of numerical examples are provided to check the effectiveness and efficiency.