Solutions Of Fractional Impulsive Differential Equations On Unbounded Domains

In this paper, we mainly consider the existence of initial value problems of impulsive fractional differential equations with infinite moments of impulse effect involving Caputo fractional derivatives on unbounded domains. First, by employing the classic method of Toneliiand the locally convex topology, we consider the impulsive differential equation as the order β satisfies0<β<1, and we derive a new existence result without the compactness-type condition; Then, by using the Krasnoselskii Theorem, we consider the impulsive functional differential equations as the order β satisfies1<β<2and we also derive a new existence result; In the end of this paper, two examples are given as the application of our conclusion.