A stability result for the determination of order in time-fractional diffusion equations

2020 ◽  
Vol 28 (3) ◽  
pp. 379-388
Author(s):  
Zhiyuan Li ◽  
Xinchi Huang ◽  
Masahiro Yamamoto
Keyword(s):  
Fractional Order ◽  
Interior Point ◽  
Eigenfunction Expansion ◽  
Stability Result ◽  
Fractional Diffusion ◽  
Measured Data ◽  
Diffusion Equations ◽  
Lipschitz Stability ◽  
Fractional Diffusion Equations

AbstractThis paper deals with an inverse problem of the determination of the fractional order in time-fractional diffusion equations from one interior point observation. We give a representation of the solution via the Mittag-Leffler function and eigenfunction expansion, from which the Lipschitz stability of the fractional order with respect to the measured data at the interior point is established.

scholarly journals Identification of points sources via time fractional diffusion equation

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6189-6201 ◽  
Author(s):  
A. Ghanmi ◽  
R. Mdimagh ◽  
I.B. Saad
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Stability Result ◽  
Fractional Diffusion ◽  
Cauchy Data ◽  
Diffusion Equations ◽  
Lipschitz Stability ◽  
Single Measurement ◽  
Fractional Diffusion Equations ◽  
Time Fractional Diffusion Equation

This article investigates the source identification in the fractional diffusion equations, by performing a single measurement of the Cauchy data on the accessible boundary. The main results of this work consist in giving an identifiability result and establishing a local Lipschitz stability result. To solve the inverse problem of identifying fractional sources from such observations, a non-iterative algebraical method based on the Reciprocity Gap functional is proposed.

scholarly journals Strong maximum principle for fractional diffusion equations and an application to an inverse source problem

2016 ◽  
Vol 19 (4) ◽  
Author(s):  
Yikan Liu ◽  
William Rundell ◽  
Masahiro Yamamoto
Keyword(s):  
Maximum Principle ◽  
Parabolic Equations ◽  
Fractional Diffusion ◽  
Uniqueness Result ◽  
Strong Maximum Principle ◽  
Diffusion Equations ◽  
Inverse Source Problem ◽  
Fractional Diffusion Equations ◽  
Parabolic Case

AbstractThe strong maximum principle is a remarkable property of parabolic equations, which is expected to be partly inherited by fractional diffusion equations. Based on the corresponding weak maximum principle, in this paper we establish a strong maximum principle for time-fractional diffusion equations with Caputo derivatives, which is slightly weaker than that for the parabolic case. As a direct application, we give a uniqueness result for a related inverse source problem on the determination of the temporal component of the inhomogeneous term.

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