Fractional diffusion and wave equations are obtained by letting α vary in (0,1) and (1,2), respectively. The corresponding Green's functions are obtained in closed form for arbitrary space dimensions in terms of Fox functions and their properties are exhibited. In particular, it is shown ...
Fractional diffusion and wave equations are obtained by letting α vary in (0,1) and (1,2), respectively. The corresponding Green's functions are obtained in closed form for arbitrary space dimensions in terms of Fox functions and their properties are exhibited. In particular, it is shown ...
分离变量法解三维的分数阶扩散-波动方程的初边值问题 Separation of variables method for fractional diffusion-wave equation with initial-boundary value problem in three dimension...
fractional diffusion-wave equationunconditional stability35R1165M06In this article, a novel compact finite difference scheme is \\mboxconstructed to solve the fractional diffusion-wave equation based on its equivalent integro-differential equation. In the temporal direction, the product trapezoidal scheme ...
H. Heydari and C. Cattani, Numerical solution of fractional sub-diffusion and time-fractional diffusion-wave equations via fractional-order Legendre functions, The European Physical Journal Plus 131, No. 8 (2016) 131-268.M. R. Hooshmandasl, M. H. Heydari, and C. Cattani, "Numer- ical ...
H Jafari,M Dehghan,K Sayevand - 《Numerical Methods for Partial Differential Equations》 被引量: 30发表: 2010年 A general solution for a fourth-order fractional diffusion--wave equation defined in a bounded domain This paper presents a general solution for a fourth-orderfractional diffusion--wav...
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 area of fractional partial differential equations has recently become prominent for its ability to accurately simulate complex physical events. The search for traveling wave solutions for fractional partial differential equations is a difficult task,
A fast compact difference scheme for the fourth-order multi-term fractional sub-diffusion equation with non-smooth solution In this paper, the H_2N_2 method and compact finite difference scheme are proposed for the fourth-order time-fractional diffusion-wave equations. In order ... D Cen,Z Wa...
The processes involving the basic phenomena of relaxation, diffusion, oscillations and wave propagation are of great relevance in physics; from a mathematical point of view they are known to be governed by simple differential equations of order 1 and 2 in time. The introduction of fractional deriva...