The subject of nonlinear dynamical systems has captured the mind of many people in the last decade, due to their wider occurrence in daily life. This subject covers many areas in the fields of science, engineering and technology. For instance, the topic covers: dynamics; non-equilibrium processes in physics; complex matter and networks; computational biology; fluctuations and random processes; self-organization; social phenomena; fractal geometry, media with self-similar properties; technology and other interesting subject close related to nonlinear dynamical system. To apprehend and forecast the forthcoming conduct of these complex problems, scientists trust mathematical replicas, which on their turn depend most of the time on mathematical tools known as differential and integral operators. One can find in the available literature two groups of differential and integral operators including classical and non-conventional. Nonetheless, with many proofs in published research papers the classical are more appropriate for classical mechanics and suppose to describe only those processes known as memoryless or Markovian, this implies, these differential operators predict the future with no memory. This is a highly misleading, as many real world problems do not follow Markovian processes, rather they mostly follow a non-Markovian scenario. To solve this problem, the second group of differential operators has been suggested and they can be identified as differential operators with singular non-local kernel, differential operators with non-singular local kernel and finally differential operators with non-singular, nonlocal kernel. The one with non-singular kernel were recently introduced and have attracted attention of researchers from all fields of science, engineering and technology. These new mathematical tools possess the following important properties as was reported in some recently published research papers:
- The derivatives have at the same time Markovian and Non-Markovian properties, while the well-known Riemann-Liouville derivative is just Markovian and the Caputo-Fabrizio derivative is non-Markovian.
- The derivative waiting time is at the same time power law, stretched exponential and Brownian motion, while Riemann-Liouville derivative is only power law and Caputo-Fabrizio only exponential decay.
- The derivative mean square displacement is a crossover from usual diffusion to sub-diffusion, while Riemann-Liouville is just power law and scale-invariant. This means the Atangana-Baleanu fractional derivative is able to describe real-world problems with different scales. This crossover behaviour is observed in many empirical systems.
- The derivative probability distribution is at the same time Gaussian and non-Gaussian, and can cross over from Gaussian to non-Gaussian without steady state. This means that the Atangana-Baleanu fractional derivative is at the same time deterministic and stochastic while the Riemann-Liouville is only deterministic.
The aim of this special issue is to report the application of these new mathematical models to non-linear dynamical systems, to advancement and progress in the modern development of non-linear dynamical theory and to report new and exciting modelling.
The scope of the special issue is as follows but not limited to application of non-singular differential operators to:
- Chaotic processes;
- Non-equilibrium problems in physics;
- Complex matter and networks;
- Computational biology;
- Fluctuations and random processes;
- Flow of fluid within media with fractal properties;
- Non-Markovian processes;
- Modelling nonlinear and dispersive effects in the medium.
数学
CAMAI 2018
ANNUAL CONFERENCE ON APPLIED MATHEMATICS AND INFORMATICS
摘要截稿: 2018-09-27
全文截稿: 2018-10-17
开会时间: 2018-11-09
会议难度: ★★★
会议地点: Bucharest
网址:http://camai.spiruharet.ro/
The Annual Conference on Applied Mathematics and Informatics is organized by Faculty of Engineering, Informatics and Geography from Spiru Haret University and by Research Center in Mathematics and Informatics, affiliated to Central Institute for Scientific Research from Spiru Haret University.
The conference is mainly addressed to researchers in mathematics, computer science and information technologies, and includes theoretical and applied mathematics and computing topics.
数学
Journal of Economic Behavior & Organization
Special Issue on Theoretical and Experimental Monetary Economics
While experimental methods are widespread in microeconomics, they are less common in macroeconomics and finance. Experimental methods, however, have important advantages also in these fields. Specifically, during the recent decades, monetary models have been built on explicit micro foundations leading to well-founded laboratory implementations.
The purpose of this special issue is to gather frontier research related to the use of experimental methods in exploring and developing monetary theory and the impact of macroeconomic policies.