Impulsive fractional partial differential equations

摘要

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 . 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.