Fractional Order Systems: From Local Behavior to Network Dynamics

Dear Colleagues, 

Fractional-order differential equations have attracted great interest for their use in modeling diverse dynamical systems in different fields, including physics, engineering, and biology. In fractional-order models, the order of the derivatives acts as a degree of freedom and can increase the accuracy of modeling. Therefore, the fractional-order models can describe the natural systems more precisely than the integer-order models. Furthermore, fractional calculus considers the memory effect, a significant factor in many processes, such as biological and financial systems. These motivations have led to substantial advances in fractional-order systems; however, many challenging problems still exist. This Special Issue deals with the unresolved problems and new advancements of fractional-order systems.

One of the hottest topics in the nonlinear dynamics field is studying the networks of coupled oscillators. The interactions among the systems in a network lead to the development of collective behaviors such as synchronization, chimera states, spiral waves, coherence resonance, etc. The emergence of these phenomena in a network relies on several factors, including the dynamics of the oscillators and the configuration of the network. Therefore, using fractional-order derivatives in the describing equations of the network can influence its collective dynamics and alter its behavior. Despite the numerous studies focusing on the behavior of a network of integer-order oscillators, less attention has been paid to the coupled fractional-order systems. Consequently, one of this Special Issue's aims is to focus on the networks of fractional-order systems.

Dr. Karthikeyan Rajagopal
Prof. Dr. Salah Mahmoud Boulaaras
Guest Editors

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