Non‐uniqueness of solution for non‐instantaneous impulsive Hilfer–Hadamard fractional‐order system

摘要

We discuss the non‐uniqueness of solution for the non‐instantaneous impulsive fractional order system (NIFrOS) involving Hilfer–Hadamard fractional derivative. For two NIFrOSs, we find their equivalent systems by reconstructing some functions to built the connection between the two NIFrOSs. And then we seek out an approximate solution and a particular solution of the NIFrOS by considering fractional derivative in its equivalent system. Finally, by computing the error between the approximate solution and exact solution, we discover that the equivalent integral equation of the NIFrOS is a integral equation with some arbitrary constants, which uncovers the non‐uniqueness of solution of the NIFrOS.