scholarly journals Uniqueness result for a fractional diffusion coefficient identification problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Fadhel Jday ◽  
Ridha Mdimagh
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Bounded Domain ◽  
Identification Problem ◽  
Fractional Diffusion ◽  
Cauchy Data ◽  
Uniqueness Result ◽  
Fractional Diffusion Equation ◽  
Coefficient Identification

Abstract In this paper, we establish an identifiability result for the coefficient identification problem in a fractional diffusion equation in a bounded domain from the observation of the Cauchy data on particular subsets of the boundary.

scholarly journals Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

scholarly journals Chebyshev collocation method for the variable-order fractional diffusion equation with a variable diffusion coefficient

2021 ◽  
Author(s):  
Rupali GUPTA ◽  
Sushil Kumar
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Fractional Power ◽  
Pseudospectral Method ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Variable Order ◽  
Maximum Absolute Error ◽  
Variable Diffusion Coefficient ◽  
Variable Diffusion

In this paper, we study the space-time variable-order fractional diffusion equation with a variable diffusion coefficient. The fractional derivatives of variable-orders are considered in the Caputo sense. We propose a numerically efficient pseudospectral method with Chebyshev polynomial as an orthogonal basis function. Also, we examine the error analysis of the given numerical approach. A variation on the maximum absolute error with the different variable orders in space and time are studied. Some illustrative examples are presented with different boundary conditions, e.g., Dirichlet, mixed, and non-local. The applicability of the method is also tested with the problem that has fractional power in solution. The results obtained from the proposed method prove the efficacy and reliability of the method.

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