The determination of the diffusion kernel on fractals and fractional diffusion equation for transport phenomena in random media

1999 ◽  
Vol 252 (3-4) ◽  
pp. 141-150 ◽  
Author(s):  
Fu-yao Ren ◽  
Jin-rong Liang ◽  
Xiao-Tian Wang
Keyword(s):  
Diffusion Equation ◽  
Random Media ◽  
Transport Phenomena ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Diffusion Kernel

Inverse source problem for a space-time fractional diffusion equation

2018 ◽  
Vol 21 (3) ◽  
pp. 844-863 ◽  
Author(s):  
Muhammad Ali ◽  
Sara Aziz ◽  
Salman A. Malik
Keyword(s):  
Diffusion Equation ◽  
Expansion Method ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Inverse Source Problem ◽  
Eigenfunction Expansion Method ◽  
Special Cases ◽  
Time Fractional Diffusion Equation

Abstract For a space-time fractional diffusion equation, an inverse problem of determination of a space dependent source term along with the solution is considered. The fractional derivatives in time and space are defined in the sense of Caputo. Due to an over-specified data at final time say T, we proved that there exists a unique solution of the inverse source problem. We use the eigenfunction expansion method to prove our main results. Several special cases of space-time fractional diffusion equations are discussed and results are interpolated from generalized results. Some examples are provided.

Sign in / Sign up

Export Citation Format

Share Document