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Abstract
Abstract This paper studies a new type of conformable non-autonomous non-instantaneous impulsive differential equations. We present the solution by a new kinds of conformable Cauchy matrix. Also, we present its some properties. Next, we respectively discuss about the existence and uniqueness of 𝓒-periodic solutions of linear homogeneous and nonhomogeneous problems. Further, we study the nonlinear problem via fixed point theorem. Examples are also given to verify theory results.
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