<p>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 dimensions. The approach is established by combining the squeezing properties and the covering of finite subspace of Banach spaces, which generalizes the method established in Hilbert spaces. The method is especially effective for functional differential equations in Banach spaces for which state decomposition of the linear part can be adopted to prove squeezing property. The theoretical results are applied to retarded functional differential equations and retarded reaction-diffusion equations for which the constructed exponential attractors possess explicit fractal dimensions that do not depend on the entropy number but only depend on the spectrum of the linear parts and Lipschitz constants of the nonlinear parts.</p>