The aim of this mini symposium is to cover advanced mathematical models, exploring their applications in dynamics, vibrations, control and fractional calculus. The study focuses on how these models can be used to describe and predict complex behavior in physical and engineering systems. The analysis of vibrations and dynamics is essential for the development of efficient and innovative technologies, while fractional calculus offers a differentiated approach to problems involving memory and non-local effects. This combination of mathematical techniques provides powerful tools for optimizing the performance and stability of diverse systems, from turbines and mechanical structures to electronic and biomedical devices.