fractional equation

Eigenvalue problems for a kind of fractional differential equations;

一类分数阶微分方程的本征值问题

The mathematics model of the systems described by fractional differential equations is proposed.

首先给出了由分数阶微分方程描述的系统的数学模型,根据对整数阶系统能控性和能观性的研究,给出了此类分数阶系统的能控性和能观性的定义,并利用两参数的Mittage-Leffler函数和Cayley-Hamilton定理分析此类分数阶系统的能控性和能观性,推导由分数阶微分方程描述的系统能控性和能观性判据。

And then, we introduce the origin of the linear fractional differential equations of multistep method, discuss their advantages and research the development of the definition of fractional derivative in detail.

本文主要研究分数阶微分方程的数值处理及稳定性的分析,分为两个部分:第一,研究了用显隐式分数阶后退的差分格式,考虑实验方程数值解的性质及稳定性分析;第二,讨论了分数阶线性多步法相容格式的零稳定性和收敛性,分析其可能的最大稳定域的估计。

Several existence results of solution for a nonlinear fractional differential equation;

非线性分数微分方程解的若干存在性结论

The main objective of the paper is to give an overview of the developments and applications of fractional differential equations.

阐述分数微分方程的发展历程、现状和应用背景,提出从推广经典微分方程角度展开研究工作的若干问题与建议。

The existence of positive solution is proved for a class of sublinear fractional differential equations where the nonlinear terms subject to the power functions.

证明了一类非线性项受幂函数控制的次线性分数微分方程的正解存在性。

Theoretical Analysis and Numerical Computation for Fractional Differential Equations;

分数阶微分方程的理论分析与数值计算

Using the Mellin transform and Fox functions,the solutions of fractional order integral equationsz(t)=∑lk=0C kk lt k+(-λ)Г(α)∫ t 0(t-s) α-1 z(s)ds α≥1and z(t)=∑2 l-1k=0C kГ(1+kα2 l)t kα/2 l +(-λ)Г(α)∫ t 0(t-s) α-1 z(s)ds l=0,1,2,… α≥0are foundz(t)=∑lk=0∑∞n=0C k(-λ) nГ(1+k+nα)t k+nα andz(t)=∑2 l-1k=0C k∑∞n=0(-λ) nГ(1+nα+kα2 l)t nα+kα2 l 

对分数阶微分方程的初值问题所对应的分数阶积分方程ｚ（ｔ）＝∑ｌｋ＝０Ｃｋｋｌｔｋ＋（－λ）Γ（α）∫ｔ０（ｔ－ｓ）α－１ｚ（ｓ）ｄｓα≥１ｚ（ｔ）＝∑２ｌ－１ｋ＝０ＣｋГ（１＋ｋα２ｌ）ｔｋα／２ｌ＋（－λ）Г（α）∫ｔ０（ｔ－ｓ）α－１ｚ（ｓ）ｄｓｌ＝０，１，２，…α≥１利用Ｍｅｌｉｎ变换和Ｆｏｘ函数求出的解为ｚ（ｔ）＝∑ｌｋ＝０∑∞ｎ＝０Ｃｋ（－λ）ｎГ（１＋ｋ＋ｎα）ｔｋ＋ｎα和ｚ（ｔ）＝∑２ｌ－１ｋ＝０Ｃｋ∑∞ｎ＝０（－λ）ｎГ（１＋ｎα＋ｋα２ｌ）ｔｎα＋ｋα２

Numerical Solution of Fractional Differential Equations by Using Legendre Wavelets

Legendre小波求分数阶微分方程的数值解

Differential Transform Method for the Fractioanl Differential Equations with Riemann-Liouville Derivative

Riemann-Liouville型分数阶微分方程的微分变换方法

Adomian Decomposition Method of Fractional Differential Equations;

分数阶微分方程的Adomian解法

Existence of Solutions for Boundary Value Problems of Fractional Differential Equations

分数阶微分方程边值问题解的存在性

L~p-STABILITY OF A CLASS NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

一类分数阶微分方程组的L~p稳定性

Theoretical Analysis and Numerical Computation for Fractional Differential Equations;

分数阶微分方程的理论分析与数值计算

Several Numerical Methods for Solving Fractional Differential Equations;

求解分数阶微分方程问题的几类数值方法

Numerical Solution and Analytic Solution for two Classes Fractional Differential Equation;

两类分数阶微分方程的近似解析解与数值解

SOLUTION FOR SYSTEM OF LINEAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS

常系数线性分数阶微分方程组的解(英文)

Fractional BDF Method for Multi-order Fractional Differential Equations

多阶分数微分方程的分数BDF方法

Reducing a Second Order Differential Equation to a Higher Equation with Constant Coefficients;

化二阶微分方程为高阶常系数微分方程

Numericalmethods for Differential Equations of Fractional Order with Time-Dependent Delay

分数阶延迟微分方程数值方法的研究

High Order Multiple Method for Fractional Ordinary Differential Equation and Numerical Method for Variable Order Fractional Diffusion Equation;

分数阶常微分方程的高阶多步法和变分数阶扩散方程的数值方法

Fractional Partial Differential Equation s Numerical Solution and Fundamental Solution;

分数阶偏微分方程的数值解及基本解

Theoretical and Numerical Investigation of Fractional Partial Differential Equations

分数阶偏微分方程的理论和数值研究

Multi-order Fractional Ordinary Differential Equation and Fractional Diffusion-wave Equation;

多阶的分数阶常微分方程和分数阶扩散—波动方程

On the Distribution of Zeros of Solutions of Second Order Differential Equations with Meromorphic Coefficients

二阶亚纯系数微分方程解的零点分布

Numerical Methods for Multi-terms Fractional-Order Ordinary Differential Equation;

求解多项分数阶常微分方程的数值方法