Related papers: Fractional Maps as Maps with Power-Law Memory
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
We show how machine learning methods can unveil the fractional and delayed nature of discrete dynamical systems. In particular, we study the case of the fractional delayed logistic map. We show that given a trajectory, we can detect if it…
We consider the evolution of logistic maps under long-term memory. The memory effects are characterized by one parameter \alpha. If it equals to zero, any memory is absent. This leads to the ordinary discrete dynamical systems. For \alpha =…
We consider the stability of periodic map with period-$2$ in linear fractional difference equations where the function is $f(x)=ax$ at even times and $f(x)=bx$ at odd times. The stability of such a map for an integer order map depends on…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
In this paper we discuss a concept of dynamic memory and an application of fractional calculus to describe the dynamic memory. The concept of memory is considered from the standpoint of economic models in the framework of continuous time…
Singular functions and, in general, H\"older functions represent conceptual models of nonlinear physical phenomena. The purpose of this survey is to demonstrate the applicability of fractional velocity as a tool to characterize Holder and…
With the discovery of new superconductors there was a running to find the justifications for the new properties found in these materials. In order to describe these new effects some theories were adapted and some others have been tried. In…
Various features of the development of individual living species, including individual humans, are programmed. Is death also programmed, and if yes, how is it implemented and what can be the underlying mechanism providing the inevitability…
In this paper we consider extensions of the gradient elasticity models proposed earlier by the second author to describe materials with fractional non-locality and fractality using the techniques developed recently by the first author. We…
According to the long-memory principle appears in fractional-order dynamical systems, analysis of these systems is commonly more complicated than those described by nonlinear ordinary differential equations. Another difficulty is due to the…
This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
In this paper, a fractional derivative with short-term memory properties is defined, which can be viewed as an extension of Caputo fractional derivative. Then, some properties of the short memory fractional derivative are discussed. Also, a…
Fractional electromagnetic field theory describes electromagnetic wave propagation through the complex, nonlocal, dissipative, fractal and also recent artificially engineered materials know as fractional metamaterials. In this theory using…
The importance of fractional time-derivative to take care of memory effects has been brought out by considering the example of a simple oscillator.
General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the non-local properties of linear and nonlinear dynamical systems are studied by using of general fractional calculus, equations with general…
Using Caputo fractional derivative of order $\alpha $ we build the fractional jet bundle of order $\alpha $ and its main geometrical structures. Defined on that bundle, some fractional dynamical systems with applications to economics are…
We consider the evolution of correlation functions in a non-Markov version of the contact model in the continuum. The memory effects are introduced by assuming the fractional evolution equation for the statistical dynamics. This leads to a…
This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…