Uniqueness Results for Fractional Integro-differential Equations with State-Dependent Nonlocal Conditions in Fréchet Spaces

Abstract

The aim of this paper is to study the existence of the unique mild solution for non-linear fractional integro-differential equations with state-dependent nonlocal condition. The result was obtained by using nonlinear alternative of Granas-Frigon for contraction in Fréchet spaces. To illustrate the result, an example is provided.

Keywords

• fractional integro-differential equations
• solution operator
• fixed point
• mild solution
• state-dependent nonlocal condition
• nonlinear alternative
• fréchet spaces
• 34g20