相关论文: Improved Matlab code for Lyapunov exponents of fra…

We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating…

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…

The concept of fractional order derivative can be found in extensive range of many different subject areas. For this reason, the concept of fractional order derivative should be examined. After giving different methods mostly used in…

We present and investigate a new type of implicit fractional linear multistep method of order two for fractional initial value problems. The method is obtained from the second order super convergence of the Gr\"unwald-Letnikov approximation…

This letter proposes a fractional-order battery model based on the Caputo definition. A closed-form time-domain solution is derived, enabling a simple recursive expression for discrete-time implementation. The model requires only the…

We introduce a numerical method, based on modified hat functions, for solving a class of fractional optimal control problems. In our scheme, the control and the fractional derivative of the state function are considered as linear…

Lyapunov functions play a fundamental role in analyzing the stability and convergence properties of optimization methods. In this paper, we propose a novel and straightforward approach for constructing Lyapunov functions for first-order…

Fractional calculus has become widely studied and applied to physical problems in recent years. As a result, many methods for the numerical computation of fractional derivatives and integrals have been defined. However, these algorithms are…

We introduce a new approach to evaluate the largest Lyapunov exponent of a family of nonnegative matrices. The method is based on using special positive homogeneous functionals on $R^{d}_+,$ which gives iterative lower and upper bounds for…

This paper focuses on the fractional difference of Lyapunov functions related to Riemann-Liouville, Caputo and Grunwald-Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for…

The coupled nonlinear space fractional Ginzburg-Landau (CNLSFGL) equations with the fractional Laplacian have been widely used to model the dynamical processes in a fractal media with fractional dispersion. Due to the existence of…

In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…

We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector…

In the context of the analysis of the chaotic properties of homogeneous and isotropic turbulence, direct numerical simulations are used to study the fluctuations of the finite time Lyapunov exponent (FTLE) and its relation to Reynolds…

We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…

This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to establish the global stability of steady states for…

A novel conformal mapping based Fractional Order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second…

The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…

We propose a high-precision numerical quadrature framework based on local Fourier extension (LFE) approximations. The method constructs, on each subinterval, a truncated-SVD stabilized local Fourier continuation of the integrand on an…

The main goal of this article is to show a new method to solve some Fractional Order Integral Equations (FOIE), more precisely the ones which are linear, have constant coefficients and all the integration orders involved are rational. The…