Abstract

We study stability properties of certain evolution equations including the fractional Cauchy problem. Under some spectral assumptions these equations are governed either by a resolvent or a regularized resolvent or a k-convoluted semigroup. We investigate the long time behavior for bounded solutions by a direct application of the ergodic theorems for regularized resolvents of Lizama and Prado (J. Approx. Theory 122:42-61, 2003), Prado (Semigroup Forum 73:243-252, 2006). We apply our results to the qualitative study of the fractional diffusion-wave equation on L p (a). © 2008 Springer Science+Business Media, LLC.