Existence and uniqueness results for initial value problem of nonlinear fractional integro‐differential equation on an unbounded domain in a weighted Banach space

Abstract

This article is concerned with the existence and uniqueness of solutions for nonlinear fractional integro‐differential equation on an unbounded domain in a weighted Banach space. New results are showed owing to the fixed point theorems of Banach and Krasnoselskii. We illustrate our results by examples to ending our theoretical study.