Mouffak Benchohra, Sara Litimein, Atika Matallah, Yong Zhou

Global Existence and Controllability for Semilinear Fractional Differential Equations with State-Dependent Delay in Fréchet Spaces

abstract:
The sufficient conditions are given ensuring the existence and the controllability of mild solutions for a semi-linear fractional differential equation with state-dependent delay in Fréchet space. We use in the study a generalization of Darboux's fixed point theorem combined with measures of non-compactness.

Mathematics Subject Classification: 34A08, 34G20, 93B05

Key words and phrases: Semiliner differential equation, controllability, state-dependent delay, fractional derivative, measures of noncompactness, almost sectorial operator