Stability Analysis for Conformable Non-instantaneous Impulsive Differential Equations

In this article, we analyze a class of conformable non-instantaneous impulsive differential equations and obtain their solutions using the non-instantaneous impulsive Cauchy matrix. We derive a suitable formula for the solution of conformable nonhomogeneous linear non-instantaneous impulsive perturbed problems and we study its exponential stability. We also investigate nonlinear non-instantaneous impulsive equations and provide some conditions needed to establish existence and uniqueness of their solutions and then we present a result which guarantees Ulam–Hyers–Rassias stability. Finally, an example is given to illustrate the theory.