Non-uniqueness of solution for initial value problem of impulsive Caputo-Katugampola fractional differential equations

Abstract

In this paper, the non-uniqueness of solution is mainly considered to the initial value problem (IVP) for the system of impulsive fractional differential equations (IFrDE) with Caputo-Katugampola derivative. The IVP for IFrDE with Caputo-Katugampola derivative is equivalent to the integral equations with an arbitrary constant, which means that the solution is non-unique. Finally, a numerical example is provided to show the main result.