Related papers: Fractional Zaslavsky and Henon Discrete Maps
In this paper the author compares behaviors of systems which can be described by fractional differential and fractional difference equations using the fractional and fractional difference Caputo Standard $\alpha$-Families of Maps as…
In this paper we present a uniform way to derive families of maps from the corresponding differential equations describing systems which experience periodic kicks. The families depend on a single parameter - the order of a differential…
This paper develops a fully discrete Fourier spectral Galerkin (FSG) method for the fractional Zakharov--Kuznetsov (fZK) equation posed on a two-dimensional periodic domain. The equation generalizes the classical ZK model by replacing the…
Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and…
The Liouville and first Bogoliubov hierarchy equations with derivatives of noninteger order are derived. The fractional Liouville equation is obtained from the conservation of probability to find a system in a fractional volume element.…
This paper considers generalizations of the functional equations that characterize the lack-of-memory properties at univariate and bivariate levels. Specifically, we extend the univariate functional equation introduced by Kaminsky (1983)…
Fractional vector calculus is the building block of the fractional partial differential equations that model non-local or long-range phenomena, e.g., anomalous diffusion, fractional electromagnetism, and fractional advection-dispersion. In…
Derivatives and integrals of non-integer order may have a wide application in describing complex properties of materials including long-term memory, non-locality of power-law type and fractality. In this paper we consider extensions of…
Fractional generalization of an exterior derivative for calculus of variations is defined. The Hamilton and Lagrange approaches are considered. Fractional Hamilton and Euler-Lagrange equations are derived. Fractional equations of motion are…
Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…
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…
The main purpose of this paper is to study both the underdamped and the overdamped dynamics of the nonlinear Helmholtz oscillator with a fractional order damping. For that purpose, we use the Grunwald-Letnikov fractional derivative…
Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
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 =…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
Fractional derivative can be defined as a fractional power of derivative. The commutator (i/h)[H, ], which is used in the Heisenberg equation, is a derivation on a set of observables. A derivation is a map that satisfies the Leibnitz rule.…
In recent years, statistical characterization of the discrete conservative dynamical systems (more precisely, paradigmatic examples of area-preserving maps such as the standard and the web maps) has been analyzed extensively and shown that,…
This paper was published in the special issue of the Journal of Inequalities and Special Functions dedicated to Professor Ivan Dimovski's contributions to different fields of mathematics: transmutation theory, special functions, integral…