摘要: In one space—and in one time—dimension a diffusion equation is solved, where the first time derivative is replaced by the λ‐fractional time derivative, 0<λ≤1. The solution is given in closed form in terms of Fox functions.关键词: Diffusion ...
fractional diffusion equationsmaximum principlefractional derivativesIn this paper we study linear and nonlinear fractional diffusion equations with the Caputo fractional derivative of non-singular kernel that has been launched recently (Caputo and Fabrizio in Prog. Fract. Differ. Appl. 1(2):73-85, ...
In this paper aRiesz space fractional diffusion equationon a finite domain is considered. 在有限区域内考虑具有初边值问题的Riesz空间分数阶扩散方程,传统扩散方程中的二阶空间导数由Riesz分数阶导数α(1<α≤2)代替就得到Riesz空间分数阶扩散方程。
We examine a numerical method to approximate to a fractional diffusion equation with the Riesz fractional derivative in a finite domain, which has second order accuracy in time and space level. In order to approximate the Riesz fractional derivative, we use the "fractional centered derivative" appro...
变分数阶扩散方程微分阶数的数值反演 Numerical Inversion for the Fractional Order in the Variable-Order Time-Fractional Diffusion Equation分数阶微积分分数阶系统分数阶控制器对于变分数阶扩散方程,给出一个隐式差分求解格式.进一步讨论由内点观测数据确定微分阶数的一个反问题,应用同伦正则化算法在不同参数取值条件...
In this article, we developed a new higher-order implicit finite difference iterative scheme (FDIS) for the solution of the two dimension (2-D) time fractional Cable equation (FCE). In the new proposed FDIS, the time fractional and space derivatives are discretized using the Caputo fractional ...
2. The time-space fractional Black–Scholes equation We solve U(x,τ) from the following time-space fractional Black–Scholes equation [7]: (2.1)CDτγU(x,τ)=(r−v)Ux(x,τ)+vDxαU(x,τ)−rU(x,τ),x∈(Bd,Bu),τ∈(0,T],where CDτγ is the Caputo fractional differential...
The following problem for the fractional diffusion-wave equations is solved: _0D~α_tu= ο ~2u ο x~2,0x1,t0,0α≤2, u(0,t;α)=0, u(1,t;α)=θ(t), u(x,0~+;α)=0, in addition u\-t(x,0~+;α)=0 as 1α≤2, where θ(t) is the Heaviside unit step function ,...
The basic properties of thisdifference operator are investigated and on its basis some difference schemesgenerating approximations of the second and forth order in space and the secondorder in time for the time fractional diffusion equation with variablecoefficients are considered. Stability of the ...
fractional diffusion equationStefan’s problemTwo Stefan's problems for the diffusion fractional equation are solved, where the fractional derivative of order alpha a (0, 1) is taken in the Caputo sense. The first one has a constant condition on x = 0 and the second presents a flux ...