Author(s)

Shanshan Gao and Yi Cheng

Corresponding Author

Yi Cheng

Abstract

This paper considers the nonlocal problem of a fractional nonlinear differential equation with nonlinear growth condition. We use the Leray-Schauder fixed theorem and some fractional inequalities, to prove the existence and uniqueness of solution for the fractional order differential system. Finally, we prove that the fractional nonlinear differential equation with nonlinear growth condition has a unique solution.

Keywords

Fractional differential equation; nonlocal condition; nonlinear growth condition; Leray-Schauder fixed theorem