The current scientific progress, the rapid development of new technologies, and the growing demand across many scientific disciplines for more accurate descriptions of observed phenomena often require fundamentally different approaches and new tools compared to those traditionally used. From a mathematical perspective, these changes represent a significant shift that calls for entirely new ways of problem formulation, solution strategies, and related algorithmic implementations.

For this reason, it is essential to continuously develop advanced theoretical frameworks with high application potential and, at the same time, to seek new opportunities for using already known results in areas where they have so far found only limited application.

Our goal is to develop modern mathematical methods and tools and to apply them in the description of selected real-world phenomena and problems that can be modelled using both continuous and discrete mathematical structures. Particular emphasis is placed on issues of solvability, stability, and robustness of the developed approaches.