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In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion model from the data observed at one single point on the boundary. We prove the unique recovery of the orders together with their…

Numerical Analysis · Mathematics 2021-11-17 Bangti Jin , Yavar Kian

This paper is concerned with an inverse problem of recovering a potential term and fractional order in a one-dimensional subdiffusion problem, which involves a Djrbashian-Caputo fractional derivative of order $\alpha\in(0,1)$ in time, from…

Analysis of PDEs · Mathematics 2021-09-22 Bangti Jin , Zhi Zhou

There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…

Analysis of PDEs · Mathematics 2019-04-08 William Rundell , Zhidong Zhang

In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian--Caputo fractional…

Numerical Analysis · Mathematics 2023-11-07 Bangti Jin , Kwancheol Shin , Zhi Zhou

In this work, we study an inverse problem of recovering a space-time dependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathematical model involves a Djrbashian-Caputo fractional derivative…

Numerical Analysis · Mathematics 2022-09-23 Bangti Jin , Zhi Zhou

In this article we study inverse problems of recovering a space-time dependent source component from the lateral boundary observation in a subidffusion model. The mathematical model involves a Djrbashian-Caputo fractional derivative of…

Numerical Analysis · Mathematics 2021-05-19 Bangti Jin , Yavar Kian , Zhi Zhou

In this work, we study an inverse problem of recovering information about the weight in distributed-order time-fractional diffusion from the observation at one single point on the domain boundary. In the absence of an explicit knowledge of…

Numerical Analysis · Mathematics 2023-01-10 Bangti Jin , Yavar Kian

The diffusion system with time-fractional order derivative is of great importance mathematically due to the nonlocal property of the fractional order derivative, which can be applied to model the physical phenomena with memory effects. We…

Analysis of PDEs · Mathematics 2021-03-24 Mengmeng Zhang , Jijun Liu

A standard inverse problem is to determine a source which is supported in an unknown domain $D$ from external boundary measurements. Here we consider the case of a time-dependent situation where the source is equal to unity in an unknown…

Numerical Analysis · Mathematics 2019-04-08 William Rundell , Zhidong Zhang

We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…

Numerical Analysis · Mathematics 2024-07-23 Siyu Cen , Kwancheol Shin , Zhi Zhou

A distributed order fractional diffusion equation is considered. Distributed order derivatives are fractional derivatives that have been integrated over the order of the derivative within a given range. In this paper sub-diffusive cases are…

Mathematical Physics · Physics 2007-05-23 Mark Naber

This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while in an incompletely known medium. We prove that the boundary…

Numerical Analysis · Mathematics 2023-07-10 Siyu Cen , Bangti Jin , Yikan Liu , Zhi Zhou

We consider a class of porous medium type of equations with Caputo time derivative. The prototype problem reads as $\Dc u=-\A u^m$ and is posed on a bounded Euclidean domain $\Omega\subset\mathbb{R}^N$ with zero Dirichlet boundary…

Analysis of PDEs · Mathematics 2024-04-03 Matteo Bonforte , Maria Gualdani , Peio Ibarrondo

We consider diffusion type equations with a distributed order derivative in the time variable. This derivative is defined as the integral in $\alpha$ of the Caputo-Dzhrbashian fractional derivative of order $\alpha \in (0,1)$ with a certain…

Mathematical Physics · Physics 2015-06-26 Anatoly N. Kochubei

In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of single point data $u(x_0,t,\omega).$ We build the…

Analysis of PDEs · Mathematics 2020-04-09 Shubin Fu , Zhidong Zhang

The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation…

Analysis of PDEs · Mathematics 2020-12-29 Ravshan Ashurov , Sabir Umarov

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Analysis of PDEs · Mathematics 2019-07-05 Yavar Kian , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

In this work we investigate an inverse problem of identifying a spatially variable order in the one-dimensional subdiffusion model from the boundary flux measurement. The model involves a generalized Caputo derivative in time, and arises in…

Analysis of PDEs · Mathematics 2024-11-28 Jiho Hong , Bangti Jin , Yavar Kian

In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…

Numerical Analysis · Mathematics 2025-08-19 Yikan Liu

The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time scales and is often referred to as {\it the\/} diffusion…

Analysis of PDEs · Mathematics 2021-01-19 Barbara Kaltenbacher , William Rundell
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