Dear Colleagues,

Since the seminal work of Fourier on periodic functions, periodicity has played a central role not only in mathematics but also in natural sciences such as physics, chemistry, and biology that deal with matter, energy, and their interrelations and transformations. Nonlinear phenomena, by contrast, are difficult to describe by mathematical analysis based on smoothness, and thus, fractional calculus has been used to model many such processes for which the standard integer-order derivatives do not work adequately. While it is well known that the classical derivative of a periodic function is a periodic function with the same period, things are different with respect to derivatives of fractional order, where the periodicity property is not maintained by the fractional derivative of periodic functions. In addition to the theoretical importance of the first result of Tavazoei on the non-periodicity of non-constant solutions of autonomous fractional-order equations, its implication on numerical analysis of autonomous fractional-order systems has become more and more serious. Moreover, since then, several works on other aspects of periodicity of fractional-order systems, such as asymptotical periodicity, has appeared as complementary to or a remedy of the unpleasant non-periodicity of fractional order systems. Similar aspects of periodicity in discrete-time systems of fractional order have also been developed. As a consequence, all reported results based on the “periodicity” of fractional-order continuous- or discrete-time autonomous systems have become questionable. A numerical approach to fractional-order systems may be carried out using several reliable numerical schemes especially designed for such systems.

This Special Issue aims to collect new perspectives on the trends in both theory and applications of stability, (non)periodicity of fractional order continuous and discrete systems, analytical and numerical approaches, and any related problems regarding (but not limited to) time-delayed systems and impulsive systems in all fields of science, as well as engineering mand multidisciplinary applications.

Prof. Dr. Michal Fečkan
Prof. Dr. Marius-F. Danca
Guest Editors

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• Fractional-order system
• Stability
• Periodic solution
• Fractional calculus