GLOBAL EXISTENCE AND CONTROLLABILITY FOR SEMILINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY IN FRéCHET SPACES

摘要

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.