Related papers: Flatness For Linear Fractional Systems With Applic…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
The Lie symmetry method is applied to derive the point symmetries for the N-dimensional fractional heat equation. We find that that the numbers of symmetries and Lie brackets are reduced significantly as compared to the nonfractional order…
The fractional quantum Hall effect remains a captivating area in condensed matter physics, characterized by strongly correlated topological order, which manifests as fractionalized excitations and anyonic statistics. Numerical simulations,…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…
This paper proposes several nonlinear control strategies for trajectory tracking of a quadcopter system based on the property of differential flatness. Its originality is twofold. Firstly, it provides a flat output for the quadcopter…
We demonstrate how the unusual mathematics of transfinite numbers, in particular a nearly perfect realization of Hilbert's famous hotel paradox, manifests in the propagation of light through fractional vortex plates. It is shown how a…
Form factor sequences of an integrable QFT can be defined axiomatically as solutions of a system of recursive functional equations, known as ``form factor equations''. We show that their solution can be replaced with the study of the…
This contribution deals with the creation of numerical models for the simulation of the dynamic characteristics of fractional-order control systems and their comparison with analytical models. We give the results of the comparison of…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
Fractals and multifractals and their associated scaling laws provide a quantification of the complexity of a variety of scale invariant complex systems. Here, we focus on lattice multifractals which exhibit complex exponents associated with…
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
In this paper, we study fractional order heat equation in higher space-time dimensions and offer specific role of heat flows in various fractional dimensions. We offer fractional solutions of the heat equations thus obtained, and examine…
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
Total energy electronic structure calculations, based on density functional theory or on the more empirical tight binding approach, are generally believed to scale as the cube of the number of electrons. By using the localisaton property of…
We show that every flat nonlinear discrete-time system with two inputs can be transformed into a structurally flat normal form by state- and input transformations. This normal form has a triangular structure and allows to read off the flat…
The nonlinear formulation developed based on von Karman's assumptions is employed to study the free vibration characteristics of functionally graded material (FGM) plates subjected to thermal environment. Temperature field is assumed to be…
We analyze the thermal conductivity of frustrated spin-1/2 chains within linear-response theory focusing on its frequency dependence at finite temperatures. Using exact diagonalization, the low-frequency limit of the thermal conductivity is…
We have studied the optical properties of gratings micro-fabricated into semiconductor wafers, which can be used for simplifying cold-atom experiments. The study entailed characterisation of diffraction efficiency as a function of coating,…
The usefulness of semi-analytical thermal models for predicting the connection between process, microstructure and properties in powder bed fusion has been well illustrated in recent years. Such an approach provides the promise of accuracy…