Related papers: A Dynamic-Order Fractional Dynamic System
Fractional-order dynamical networks are increasingly being used to model and describe processes demonstrating long-term memory or complex interlaced dependencies amongst the spatial and temporal components of a wide variety of dynamical…
This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical of classical integral and gradient formulations, under a single frame-invariant framework.…
There has recently been considerable interest in using a nonstandard piecewise approximation to formulate fractional order differential equations as difference equations that describe the same dynamical behaviour and are more amenable to a…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of…
In the paper we study the subject of positivity of systems with sequential fractional difference. We give formulas for the unique solutions of systems in linear and semi-linear cases. The positivity of systems is considered.
A novel probabilistic approach for the design of mechanical structures with friction interfaces is proposed. The objective function is defined as the probability that a specified performance measure of the forced vibration response is…
Quantum optomechanics describes the interaction between a confined field and a fluctuating wall due to radiation pressure. The dynamics of this system is typically understood using perturbation theory up to second order in the small…
We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of…
We consider a conflict-controlled dynamical system described by a nonlinear ordinary fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1).$ Basing on the finite-difference Gr\"{u}nwald-Letnikov…
Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by fractional-order than integer-order derivatives, and many methods are developed to solve the problem of fractional…
Identification of fractional order systems is considered from an algebraic point of view. It allows for a simultaneous estimation of model parameters and fractional (or integer) orders from input and output data. It is exact in that no…
We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…
In this paper, we use the fractional calculus to discuss the fractional mechanics, where the time derivative is replaced with the fractional derivative of order $\nu$. We deal with the motion of a body in a resisting medium where the…
Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of…
This paper considers the problem of robust stability and stabilization for linear fractional-order system with nonlinear uncertain parameters, with fractional order 0<a<2. A dynamic output feedback controller, with predetermined order, for…
Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a…
Complex-dynamical fractal is a hierarchy of permanently, chaotically changing versions of system structure, obtained as the unreduced, causally probabilistic general solution of arbitrary interaction problem (physics/0305119,…
This paper deals with feedback control of fractional-order Chua's system. The fractional-order Chua's system with total order less than three which exhibit chaos as well as other nonlinear behavior and theory for control of chaotic systems…
The presence of a phase transition in a finite system can be deduced, together with its order, from the shape of the distribution of the order parameter. This issue has been extensively studied in multifragmentation experiments, with…