Title: On the initial value problem of impulsive differential equation involving Caputo-Katugampola fractional derivative of order q ∈ (1, 2)

Authors: Xian-Min Zhang

Addresses: School of Mathematics and Statistics, Yangtze Normal University, Fuling, Chongqing, 408100, China

Abstract: This paper mainly focuses on the non-uniqueness of solution to the initial value problem (IVP) of impulsive fractional differential equations (IFrDE) with Caputo-Katugampola derivative (of order q ∈ (1, 2)). The system of impulsive higher order fractional differential equations may involve two different kinds of impulses, and the obtained result shows that its equivalent integral equations include two arbitrary constants, which means that its solution is non-unique. Next, two numerical examples are used to show the non-uniqueness of solution for the IVP of IFrDE.

Keywords: fractional differential equation; IFrDE; impulsive fractional differential equation; impulse; Caputo-Katugampola derivative; differential equations with impulses; initial value problems.

DOI: 10.1504/IJDSDE.2022.122526

International Journal of Dynamical Systems and Differential Equations, 2022 Vol.12 No.1, pp.75 - 105

Received: 15 Nov 2018
Accepted: 03 Sep 2019
Published online: 03 May 2022 *