Impulsive fractional partial differential system and its correct
integral solution
Abstract
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.