scholarly journals A space–time spectral collocation algorithm for the variable order fractional wave equation

SpringerPlus ◽  
2016 ◽  
Vol 5 (1) ◽  
Author(s):  
A. H. Bhrawy ◽  
E. H. Doha ◽  
J. F. Alzaidy ◽  
M. A. Abdelkawy
Keyword(s):  
Wave Equation ◽  
Space Time ◽  
Variable Order ◽  
Spectral Collocation ◽  
Fractional Wave Equation

scholarly journals On the Fractional Wave Equation

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 874
Author(s):  
Francesco Iafrate ◽  
Enzo Orsingher
Keyword(s):  
Brownian Motion ◽  
Wave Equation ◽  
Wave Equations ◽  
Stable Process ◽  
Space Time ◽  
Probabilistic Interpretation ◽  
Symmetric Stable Process ◽  
Fractional Wave Equation ◽  
Fractional Wave Equations ◽  
Time Fractional Wave Equation

In this paper we study the time-fractional wave equation of order 1 < ν < 2 and give a probabilistic interpretation of its solution. In the case 0 < ν < 1 , d = 1 , the solution can be interpreted as a time-changed Brownian motion, while for 1 < ν < 2 it coincides with the density of a symmetric stable process of order 2 / ν . We give here an interpretation of the fractional wave equation for d > 1 in terms of laws of stable d−dimensional processes. We give a hint at the case of a fractional wave equation for ν > 2 and also at space-time fractional wave equations.

scholarly journals Space-Time Estimates on Damped Fractional Wave Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Jiecheng Chen ◽  
Dashan Fan ◽  
Chunjie Zhang
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Initial Data ◽  
Linear Equations ◽  
Space Time ◽  
Regularity Conditions ◽  
Fractional Wave Equation ◽  
Time Estimates ◽  
Almost Everywhere ◽  
The Cauchy Problem

We obtain space-time estimates on the solutionu(t,x)to the Cauchy problem of damped fractional wave equation. We mainly focus on the linear equation. The almost everywhere convergence of the solution to linear equations ast→0+is also studied, with the initial data satisfying certain regularity conditions.

scholarly journals SPACE-TIME SPECTRAL COLLOCATION ALGORITHM FOR THE VARIABLE-ORDER GALILEI INVARIANT ADVECTION DIFFUSION EQUATIONS WITH A NONLINEAR SOURCE TERM

2017 ◽  
Vol 22 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Mohamed A. Abd-Elkawy ◽  
Rubayyi T. Alqahtani
Keyword(s):  
Source Term ◽  
Dimensional Space ◽  
Space Time ◽  
Variable Order ◽  
Spectral Collocation ◽  
Nonlinear Source ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Collocation Technique ◽  
Collocation Scheme

This paper presents a space-time spectral collocation technique for solving the variable-order Galilei invariant advection diffusion equation with a nonlinear source term (VO-NGIADE). We develop a collocation scheme to approximate VONGIADE by means of the shifted Jacobi-Gauss-Lobatto collocation (SJ-GL-C) and shifted Jacobi-Gauss-Radau collocation (SJ-GR-C) methods. We successfully extend the proposed technique to solve the two-dimensional space VO-NGIADE. The discussed numerical tests illustrate the capability and high accuracy of the proposed methodologies.

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