On piecewise continuous solutions of higher order impulsive fractional differential equations and applications

Abstract

For impulsive differential equations with fractional order, we show that the formula of solutions in cited papers are incorrect. We then give exact piecewise continuous solutions (the explicit solutions) of two classes of fractional differential equations of order α∈(n−1,n) involving Caputo derivatives and Riemann–Liouville derivatives. Apply our results to obtain existence of solutions of two classes of initial value problems of singular impulsive fractional differential equations. Examples are presented to illustrate the main theorems.