The linear Oskolkov system of non-zero order in the Avalos–Triggiani problem

The Avalos–Triggiani problem for a linear Oskolkov system of non-zero order and a system of wave equations is investigated. The mathematical model contains a linear Oskolkov system of non-zero order and a wave vector equation corresponding to some structure immersed in the Kelvin–Voight incompressible viscoelastic fluid. The theorem of the existence of the unique solution to the Avalos–Triggiani problem for the indicated systems is proved using the method proposed by the authors of this problem. The results of this article generalize the results received earlier.