Existence of solutions for fractional impulsive neutral functional differential equations with infinite delay

In this paper, we first introduce a class of impulsive neutral fractional functional differential equations which arise from many practical applications such as in viscoelasticity and electrochemistry. After providing a natural formula of solutions for the equations, we then give an existence theorem of the solutions by using the Hausdorff's measure of noncompactness and the theory of Mönch. As a result, the existence theory provides a theoretical basis for exploring the solutions of such kinds of differential equations.