Some Existence Results for High Order Fractional Impulsive Differential Equation on Infinite Interval

Abstract EN

In this paper, we consider the high order impulsive differential equation on infinite interval D0+αut+ft,ut,J0+βut,D0+α−1ut=0, t∈0,∞∖tkk=1m△utk=Ikutk, t=tk,k=1,…,mu0=u′0=⋯=un−20=0,D0+α−1u∞=u0 By applying Schauder fixed points and Altman fixed points, we obtain some new results on the existence of solutions.

The nonlinear term of the equation contains fractional integral operator Jβut and lower order derivative operator D0+α−1ut.

An example is presented to illustrate our results.