scholarly journals Finite difference method for solving the space-time fractional wave equation in the Caputo form

2015 ◽  
pp. 55-63 ◽  
Author(s):  
Elham Afshari ◽  
Behnam Sepehrian ◽  
Ali Mohamad Nazari
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Space Time ◽  
Fractional Wave Equation ◽  
Time 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.

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