o:28779 Internal Variable Theory in Viscoelasticity: Fractional Generalizations and Thermodynamical Restrictions en 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. Keywords: fractional calculus; internal variables; thermodynamical admissibility 1552099 10.3390/math10101708 1552101 2227-7390 2023-04-12T08:28:27.431Z 44 no 46 Teodor Atanacković Državni univerzitet u Novom Pazaru 0000-0002-8714-1388 Ćemal Dolićanin person 0000-0003-4830-1454 Enes Kačapor person 0000-00001-6658-051X application/pdf 351833 https://phaidrabg.bg.ac.rs/o:28779 no yes 1 70 92000001 20A01 Mathematics MDPI 10 10 2022