Title: Non-uniqueness of solution for initial value problem of impulsive fractional partial differential equations

Authors: Xian-Min Zhang

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

Abstract: This paper mainly researches the formulas of solution for the initial value problems (IVPs) of two impulsive fractional partial differential equations (IFrPDEs). For these IVPs of IFrPDEs, some properties of their solutions are found, which uncover that the formulas of solutions given by some cited papers are inappropriate due to not meeting these properties. Next, by analysing errors between the approximate solutions and exact solutions, two new formulas of solution of these IVPs of IFrPDEs are discovered that are the integral equations with some undetermined differentiable functions, which illustrate the non-uniqueness of solution of the IVPs of IFrPDEs to be expounded by two examples.

Keywords: non-uniqueness of solution; impulsive fractional partial differential equations; IVPs; initial value problems.

DOI: 10.1504/IJDSDE.2022.126527

International Journal of Dynamical Systems and Differential Equations, 2022 Vol.12 No.4, pp.316 - 338

Accepted: 07 Mar 2021
Published online: 28 Oct 2022 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article