Fractional Calculus: Theory and Applications

Fractional calculus (FC) has emerged as a beneficial tool for the study of dynamical systems. This is due to the fact that fractional-order (FO) operators capture the memory of all past events, leading to better descriptions of real-world phenomena than their integer-order counterparts. From this perspective, the systems modelling and control of FO with applications of real-world problems is of key significance. Despite the extraordinary advances in FC, new theoretical developments and applications are still needed to accurately describe or control many systems and signals characterized by chaos, bifurcations, criticality, symmetry, memory, scale invariance, fractality, fractionality, and other rich features.