Theory, Applications, and Numerics of Fractional-Order Dynamical Systems: An Overview of the Special Issue

Fractional calculus provides a framework for describing nonlocal evolution and memory effects, and has become an important tool across mathematical analysis, computation, and applications. This special issue of Fractals brings together 33 contributions spanning fractional operators and their qualitative properties, existence and stability theory, bifurcation in delayed epidemic models, nonlinear and stochastic waves, fractional diffusion and transport, and numerical algorithms. The applications range from biochemical and epidemiological models to optical propagation, fluid flow, electroosmosis, electrical circuits, and environmental pollution. A small number of contributions address closely related mathematical or computational topics without formulating a fractional-order dynamical system. This overview organizes the papers into five complementary themes, highlights their principal methods and results, and identifies cross-cutting challenges concerning operator selection, mathematical validation, numerical reliability, and application-led modeling.