The analytical solution and numerical solutions for a two-dimensional multi-term time fractional diffusion and diffusion-wave equation

2019 ◽  
Vol 345 ◽  
pp. 515-534 ◽  
Author(s):  
Shujun Shen ◽  
Fawang Liu ◽  
Vo V. Anh
Keyword(s):  
Wave Equation ◽  
Analytical Solution ◽  
Numerical Solutions ◽  
Fractional Diffusion ◽  
Two Dimensional ◽  
Diffusion Wave ◽  
And Diffusion

scholarly journals On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equatio

2017 ◽  
Author(s):  
Yuri Luchko
Keyword(s):  
Wave Equation ◽  
Fundamental Solution ◽  
Open Problem ◽  
Special Functions ◽  
Dimensional Space ◽  
Fractional Diffusion ◽  
Two Dimensional ◽  
Diffusion Wave ◽  
Space And Time ◽  
Mellin Convolution

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

Sign in / Sign up

Export Citation Format

Share Document