It is found that there are two piecewise functions satisfy the conditions in the impulsive fractional partial differential system (IFrPDS), which deduce that the three different integral solutions of the IFrPDS given in the cited papers are inappropriate. Next, by applying two limit properties of the IFrPDS and the properties of piecewise function, the new formula of solution of the IFrPDS is discovered that is the integral equation with an arbitrary continuously differentiable function of t on [0 ,c] to reveal the non-uniqueness of the IFrPDE’s solution. Finally, an example is provided to expound the computation of the solution of the IFrPDS.