In this paper, we study a complete second-order integro-differential operator equation in Hilbert space. The difference-type kernel of an integral perturbation is holomorphic semigroup bordered by unbounded operators. asymptotic behavior solutions studied. Asymptotic formulas for are proved the case when right-hand side close to almost periodic function. obtained applied problem forced longitud...

The paper is devoted to the construction of effective acoustic equations for a two-phase layered viscoelastic material described by Kelvin–Voigt model with fractional time derivatives. For this purpose, theory two-scale convergence and Laplace transform respect are used. It shown that partial integro-differential derivatives exponential convolution kernels. In order find coefficients kernels th...

In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts the...

In this study, a realistic model for dynamic instability of embedded single-walled nanotubes (SWCNTs) conveying pulsating fluid is presented considering the viscoelastic property of the nanotubes using Kelvin–Voigt model. SWCNTs are placed in longitudinal magnetic fields and modeled by sinusoidal shear deformation beam theory (SSDBT) as well as modified couple stress theory. The effect of slip ...

In this paper, we study the stability problem of a star-shaped network elastic strings with local Kelvin-Voigt damping. Under assumption that damping coefficients have some singularities near transmission point, prove semigroup corresponding to system is polynomially stable and decay rates depend on speed degeneracy. This result improves rate associated an earlier Z. Liu Q. Zhang in [21] involv...