English
Related papers

Related papers: Inverse problems for diffusion equation with fract…

200 papers

This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the…

Analysis of PDEs · Mathematics 2026-05-05 Erkinjon Karimov , Muzaffar Toshpulatov

In the Hilbert space $H$, the inverse problem of determining the right-hand side of the abstract subdiffusion equation with the fractional Caputo derivative is considered. For the forward problem, a non-local in time condition $u(0)=u(T)$…

Analysis of PDEs · Mathematics 2023-08-11 Ravshan Ashurov , Marjona Shakarova

This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…

Mathematical Physics · Physics 2014-09-11 R. K. Saxena , A. M. Mathai , H. J. Haubold

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

This paper is devoted to the study of the inverse problem of determining the right-hand side of the subdiffusion equation with the Caputo derivative with respect to time. In our case, the inverse problem consists in restoring the…

Analysis of PDEs · Mathematics 2025-05-20 R. R. Ashurov , O. T. Mukhiddinova

We study the inverse problem of recovering the order and the diffusion coefficient of an elliptic fractional partial differential equation from a finite number of noisy observations of the solution. We work in a Bayesian framework and show…

Analysis of PDEs · Mathematics 2017-06-28 Nicolas Garcia Trillos , Daniel Sanz-Alonso

In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.

Analysis of PDEs · Mathematics 2019-11-14 Suman Kumar Sahoo , Manmohan Vashisth

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…

Analysis of PDEs · Mathematics 2019-04-15 Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

We consider a class of nonlinear fractional equations having the Caputo fractional derivative of the time variable $t$, the fractional order of the self-adjoint positive definite unbounded operator in a Hilbert space and a singular…

Analysis of PDEs · Mathematics 2020-02-18 Nguyen Minh Dien , Erkan Nane , Dang Duc Trong

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

We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…

Analysis of PDEs · Mathematics 2022-03-30 Li Li

This article primarily aims at introducing a novel operational calculus of Mikusi\'nski's type for the Dzherbashian-Nersesian operator. Using this calculus, we are able to derive exact solutions for the forward and backward source problems…

Analysis of PDEs · Mathematics 2024-02-27 Anwar Ahmad , Muhammad Ali , Salman A. Malik

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

This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the…

Mathematical Physics · Physics 2014-09-09 R. K. Saxena , A. M. Mathai , H. J. Haubold

This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the…

Analysis of PDEs · Mathematics 2012-10-05 R. K. Saxena , A. M. Mathai , H. J. Haubold

This paper is concerned with the inverse problem on determining an orbit of the moving source in a fractional diffusion(-wave) equations in a connected bounded domain of $\mathbb R^d$ or in the whole space $\mathbb R^d$. Based on a newly…

Analysis of PDEs · Mathematics 2020-02-06 Guanghui Hu , Yikan Liu , Masahiro Yamamoto

We study two new classes of inverse problems for a time-switched system in which a fractional wave equation (with Caputo derivative of order $\alpha \in (1,2)$) governs the dynamics on the interval $[0,a)$, and a fractional diffusion…

Analysis of PDEs · Mathematics 2026-05-26 E. T. Karimov , N. A. Murolimova

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

As it is known various dynamical processes can be modeled through the systems of time-fractional order pseudo-differential equations. In the modeling process one frequently faces with determining the adequate orders of time-fractional…

Analysis of PDEs · Mathematics 2021-07-21 Ravshan Ashurov , Sabir Umarov

In this study, the existence results of solution is given for fractional p-Laplacian Stum-Liouville problem for diffusion operator of order with impulsive conditions. The derivatives are described in Riemann-Liouville and Caputo sense. The…

Classical Analysis and ODEs · Mathematics 2018-02-13 Funda Metin Turk , Erdal Bas