eng All rights reserved Abstract: Here, we study the internal variable approach to viscoelasticity. First, we generalize the classical approach by introducing a fractional derivative into the equation for time evolution of the internal variables. Next, we derive restrictions on the coefficients that follow from the dissipation inequality (entropy inequality under isothermal conditions). In the example of wave propagation, we show that the restrictions that follow from entropy inequality are sufficient to guarantee the existence of the solution. We present a numerical solution to the wave equation for several values of the parameters. https://phaidrabg.bg.ac.rs/o:28779 doi:10.3390/math10101708 ISSN: 2227-7390 Atanacković, Teodor Dolićanin, Ćemal Kačapor, Enes Mathematics MDPI 10(10) Keywords: fractional calculus; internal variables; thermodynamical admissibility application/pdf 351833 bytes info:eu-repo/semantics/article 2022 Internal Variable Theory in Viscoelasticity: Fractional Generalizations and Thermodynamical Restrictions