Abstract: By using the theory of operator semigroup, estimation technique of noncompact measure and Darbo’s fixed point theorem,
we studied the existence of mild solution for conformable fractional non-instantaneous impulsive differential equation with nonlocal problem. Under the condition that the nonlinear term satisfied the  appropriate growth condition and noncompactness measure condition, and  the nonlocal term and non-instantaneous impulsive function satisfied the  Lipschitz condition, we obtained the existence result of solution of the problem, and gave  an example  to illustrate the effectiveness of the result.

Key words: fractional differential equation, operator semigroup, noninstantaneous impulse,  , mild solution, noncompact measure