基于 Caputo 和 Caputo-Fabrizio 分数阶算子的三物种捕食-被捕食模型

High order algorithms for Fokker-Planck equation with Caputo-Fabrizio fractional derivative

Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures with different scales. Extending the discretizations for fractional substantial calculus [Chen and Deng, \emph{ ESAIM: M2AN.} \textbf{49}, (2015), 373--394], we first provide the numerical discretizations of the Caputo-Fabrizio fractional derivative with the global truncation error $\mathcal{O}(τ^ν)$ $ (ν=1,2,3,4)$. Then we use the derived schemes to solve …

Finite difference/spectral approximations for the two-dimensional time Caputo-Fabrizio fractional diffusion equation

The main contribution of this work is to construct and analyze stable and high order schemes to efficiently solve the two-dimensional time Caputo-Fabrizio fractional diffusion equation. Based on a third-order finite difference method in time and spectral methods in space, the proposed scheme is unconditionally stable and has the global truncation error $\mathcal{O}(τ^3+N^{-m})$, where $τ$, $N$ and $m$ are the time step size, polynomial degree and regularity in the space variable of the exact solution, respectively. It should be noted that the global truncation error $\mathcal{O}(τ^2+N^{-m})$ i…

一种用于具有时间Caputo-Fabrizio分数导数的二维空间分数扩散方程的二阶准确方案

A second-order accurate scheme for two-dimensional space fractional diffusion equations with time Caputo-Fabrizio fractional derivative

本文提出并分析了一种用于描述粒子进行异常运动时具有指数Debye模式且无时间跳跃的粒子分布模型的二阶方案，该模型具有幂律跳跃长度。该方案在理论上和数值上均被证明是无条件稳定的，并具有非零初始条件的二阶全局截断误差，同时获得了最优估计。

具有Caputo-Fabrizio导数的多项时间分数阶扩散方程的高效数值方法

Efficient numerical method for multi-term time-fractional diffusion equations with Caputo-Fabrizio derivatives

本文针对多项Caputo-Fabrizio时间分数阶扩散方程，提出结合快速有限差分与Legendre谱配点法的高效数值格式，实现低存储、低计算复杂度，并证明其无条件稳定且具有二阶时间收敛精度。

About Convergence and Order of Convergence of some Fractional Derivatives

In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider some errors given by $\left|\left| D^{1-\al}f -f'\right|\right|_p$ for p=1 and $p=\infty$ and we prove that for both Caputo and Caputo Fabrizio operators the order of convergence is a positive real r, 0<r<1. Finally, we compare the speed of convergence between Caputo and Caputo-Fabrizio operators obtaining that they a related by the Digamma function.

具有混合Mittag-Leffler-Caputo-Fabrizio算子的分数阶SVIR流行病模型的结构保持格式

Structure-Preserving Schemes for a Fractional SVIR Epidemic Model with a Hybrid Mittag-Leffler-Caputo-Fabrizio Operator

提出基于混合MLCF分数阶算子的SVIR模型，证明解的正性和有界性，分析基本再生数和稳定性，并开发保持定性性质的θ加权非标准有限差分方法。