The non-uniqueness of solution for initial value problem of impulsive differential equations involving higher order Katugampola fractional derivative

Abstract

AbstractIn this paper we consider the initial value problem for some impulsive differential equations with higher order Katugampola fractional derivative (fractional order $q \in (1,2]$q∈(1,2]). The systems of impulsive higher order fractional differential equations can involve one or two kinds of impulses, and by analyzing the error between the approximate solution and exact solution it is found that these impulsive systems are equivalent to some integral equations with one or two undetermined constants correspondingly, which uncover the non-uniqueness of solution to these impulsive systems. Some numerical examples are offered to explain the obtained results.