Nonlinear Dynamics in Complex Systems via Fractals and Fractional Calculus

Dear Colleagues,

Nowadays, advances in the knowledge of nonlinear dynamical systems and processes as well as their unified repercussions allow us to include some typical complex phenomena taking place in nature, from nanoscale to galactic scale, in a unitary comprehensive manner. After all, any of these systems called generic dynamical systems, chaotic systems or fractal systems have something essential in common and can be considered to belong to the same class of complex phenomena, discussed here. The available physical, biological and financial data and technological (mechanical or electronic devices) complex systems can be managed by the same conceptual approach, both analytically and through a computer simulation, using effective nonlinear dynamics methods. Currently, the utilization of fractional-order partial differential equations in real physical systems is commonly encountered in the fields of theoretical science and engineering applications. This means that the productive, efficacious computational tools required for analytical and numerical estimations of such physical models, and our reliance on their development in referenced works, are welcome. Chaotic instabilities in the mathematical physics theory, fractal-type spatiotemporal behaviors in the field theory, nonlinear dynamic processes in plasma complex structures, fractional calculus and novel algorithms to solve fractional-order derivatives of classic problems are expected.

Prof. Dr. Viorel-Puiu Paun
Guest Editor

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