Zener Model with General Fractional Calculus: Thermodynamical Restrictions

We studied a Zener-type model of a viscoelastic body within the context of general fractional calculus and derived restrictions on coefficients that follow from the dissipation inequality, which is the entropy inequality under isothermal conditions. We showed, for a stress relaxation and a wave propagation, that the restriction that follows from the entropy inequality is sufficient to guarantee the existence and uniqueness of the solution. We presented numerical data related to the solution of a wave equation for several values of parameters.

Automated summary

We studied a Zener-type model of a viscoelastic body using general fractional calculus and derived restrictions on coefficients based on the dissipation inequality. We showed that for stress relaxation and wave propagation, the restriction derived from the entropy inequality is sufficient to ensure the existence and uniqueness of the solution. Numerical data related to the solution of a wave equation for different parameter values were presented.