Wave Equations, Fractional Derivatives, and a New Instance of the Lack of Robustness of Velocity Feedbacks

Due to the attenuation of disturbances under integration, it has been proposed that the time derivative of order in the stabilizing feedback of a hyperbolic system be replaced with Caputo fractional derivatives of lower order. It has already been noted that in this way exponential stability is not preserved. We first complement this result. We then prove that even dissipativity is not preserved if the Caputo fractional derivative has to be numerically computed.