Successive iterations and positive extremal solutions for a Hadamard type fractional integro-differential equations on infinite domain

Abstract

A Hadamard type fractional integro-differential equation on infinite intervals is considered. By using monotone iterative technique, we not only get the existence of positive solutions, but also seek the positive minimal and maximal solutions and get two explicit monotone iterative sequences which converge to the extremal solutions. At last, to illustrative the main result, an example is also discussed.