A class of fractional order systems with not instantaneous impulses

This paper is concerned with a kind of fractional order systems with Caputo-Hadamard derivative (of order q ϵ C and R(q) ϵ (1, 2)) and not instantaneous impulses. The obtained result uncovers that there exists a general solution for these impulsive systems, which means that the state trajectory of these impulsive systems is non-unique, and it is expounded by a numerical example.