Well-posedness for the fourth-order Moore-Gibson-Thompson equation in the class of Banach-space-valued Holder-continuous functions

[EN] In this work, we provide a full characterization of well-posedness in vector-valued Holder continuous function spaces for a fourth-order abstract evolution equation arising from the Moore-Gibson-Thompson equation with memory using operator-valued C-alpha-Fourier multipliers. We illustrate our results by providing an example based on the fourth order Moore-Gibson-Thompson equation with Dirichlet boundary conditions.