Fractional Burgers wave equation on a finite domain

Dynamic response of the one-dimensional viscoelastic rod finite length, that has one end fixed and other subject to prescribed either displacement or stress, is analyzed by analytical means Laplace transform, yielding stress an arbitrary rod's point as a convolution boundary forcing solution kernel. Thermodynamically consistent Burgers models are adopted constitutive equations describing mechanical properties rod. Short-time asymptotics implies wave propagation speed in case second class models, contrary first models. Moreover, model yield quite classical shapes time profiles resulting from assumed Heaviside function, while responses resemble sequence excitation relaxation processes.