On the Critical Strip of the Riemann zeta Fractional Derivative

The α-order fractional derivative of the Dirichlet η function is computed in order to investigate the behavior of the fractional derivative of the Riemann zeta function ζ(α) on the critical strip. The convergence of η(α) is studied. In particular, its half-plane of convergence gives the possibility to better understand the ζ(α) and its critical strip. As an application, two signal processing networks, corresponding to η(α) and to its Fourier transform respectively, are shortly described.