  The aim of this paper is to propose a new method to construct exponential
attractors for infinite dimensional dynamical systems in Banach spaces with
explicit fractal dimension. The approach is established by combing the
squeezing properties and the covering of finite subspace of Banach spaces,
which generalize the method established in Hilbert spaces. The constructed
exponential attractors possess explicit fractal dimensions which do not depend
on the entropy number but only depend on the spectrum of the linear part and
Lipschitz constant of the nonlinear part. The method is especially effective
for functional differential equations in Banach spaces for which sate
decomposition of the linear part can be adopted to prove squeezing property.
The theoretical results are applied to the retarded functional differential
equation and retarded reaction-diffusion equations.
