相关论文: Dynamics with Low-Level Fractionality

Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…

Anomalous relaxation and diffusion processes have been widely characterized by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to the singular memory kernel that…

Fractional differential calculus is a mathematical tool that has found applications in the study of social and physical behaviors considered ``anomalous''. It is often used when traditional integer derivatives models fail to represent cases…

We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides…

Through duality it is possible to transform left fractional operators into right fractional operators and vice versa. In contrast to existing literature, we establish integration by parts formulas that exclusively involve either left or…

Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…

The goal of this communication is to propose a generalized notion of the "traditional derivative". This generalization includes the fractional derivatives such as the Riemann-Liouville, Gruenwald-Letnikov, Weyl, Riesz, Caputo, Marchaud…

A unified approach has been developed to study nonlinear dynamics of a 1D lattice of particles with long-range power-law interaction. A classical case is treated in the framework of the generalization of the well-known Frenkel-Kontorova…

The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…

This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…

Fractional variation is defined as the limit of the difference quotient of the increments of a function and its argument raised to a fractional power. Fractional velocity can be suitable for characterizing singular behavior of derivatives…

This review article provides a concise summary of one- and two-dimensional models for the propagation of linear and nonlinear waves in fractional media. The basic models, which originate from fractional quantum mechanics and more…

We consider the fractional generalization of nonholonomic constraints defined by equations with fractional derivatives and provide some examples. The corresponding equations of motion are derived using variational principle.

Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…

We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate…

The idea of fractional derivatives has a long history that dates back centuries. Apart from their intriguing mathematical properties, fractional derivatives have been studied widely in physics, for example in quantum mechanics and generally…

This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…

Fractional mechanics describes both conservative and non-conservative systems. The fractional variational principles gained importance in studying the fractional mechanics and several versions are proposed. In classical mechanics the…

We consider some possible approaches to the fractional-order generalization of definition of variation (functional) derivative. Some problems of formulation of a fractional-order variational derivative are discussed. To give a consistent…

In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional…