Impulsive fractional partial differential equations

This paper deals with Cauchy problem for a class of impulsive partial hyperbolic differential equations involving the Caputo derivative. Our first purpose is to show that the formula of solutions in cited papers are incorrect. Next, we reconsider a class of impulsive fractional partial hyperbolic differential equations and introduce a correct formula of solutions for Cauchy problem in Rn. Further, some sufficient conditions for existence of the solutions are established by applying fixed point method. At last, we consider the Cauchy problem in a Banach space via the technique of measures of noncompactness and Mönch's fixed point theorem. Some examples are given to illustrate our results.