Monotone iterative technique for neutral fractional differential equation with infinite delay

Abstract

In this paper, we employ the method of lower and upper solutions coupled with the monotone iterative technique to obtain existence and uniqueness of extremal mild solutions to neutral fractional differential equation with infinite delay in an ordered Banach space. The results are obtained by using the theory of fractional calculus, monotone iterative technique, measure of noncompactness, and semigroup theory. Finally, we discuss an example to illustrate our results. Copyright © 2016 John Wiley & Sons, Ltd.