Existence and stability analysis of solutions for periodic conformable differential systems with non-instantaneous impulses

This paper focuses on analyzing the existence and stability of solutions for periodic conformable systems with non-instantaneous impulses. First, we define the notion of the conformable Cauchy matrix to present solutions and demonstrate fundamental characteristics including periodicity and exponential estimation. Moreover, the effect of the non-instantaneous impulses on the exponential stability is comprehensively analyzed. Next, by applying the constant variation method, we can derive the solution for the linear nonhomogeneous system with non-instantaneous impulses. In addition, the existence of periodic solutions for the given linear nonhomogeneous system is investigated. Further, the conditions required to guarantee the existence and uniqueness of the periodic solutions for nonlinear systems are provided.