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In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from a final observation. We first drive the…

Analysis of PDEs · Mathematics 2014-01-15 Abeer Aldoghaither , Taous-Meriem Laleg-Kirati , Da-Yan Liu

A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…

Materials Science · Physics 2022-12-08 Guglielmo Macrelli

In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…

Dynamical Systems · Mathematics 2016-10-27 Nicholas Apostolopoulos , Fernando Ortega , Grigoris Kalogeropoulos

This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…

Numerical Analysis · Mathematics 2025-02-25 Yun Zhang , Xiaoli Feng , Xiongbin Yan

In this paper the inverse problem of determining the fractional orders in mixed-type equations is considered. In one part of the domain the considered equation is the subdiffusion equation with a fractional derivative in the sense of…

Analysis of PDEs · Mathematics 2024-06-03 R. R. Ashurov , R. T. Zunnunov

We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…

We study the unique existence of weak solutions for initial boundary value problems associated with different class of fractional diffusion equations including variable order, distributed order and multiterm fractional diffusion equations.…

Analysis of PDEs · Mathematics 2021-11-12 Yavar Kian

In this paper, we obtained the sufficient conditions for the existence of solutions to the discrete boundary value problems of fractional difference equation depending on parameters. We use Krasnoselskii fixed point theorem to establish the…

Classical Analysis and ODEs · Mathematics 2020-04-01 Deepak B. Pachpatte , Arif S. Bagwan , Amol D. Khandagale

In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…

Analysis of PDEs · Mathematics 2023-11-03 Xiaoli Feng , Qiang Yao , Peijun Li , Xu Wang

In this paper we prove uniqueness for an inverse boundary value problem (IBVP) arising in electrodynamics. We assume that the electromagnetic properties of the medium, namely the magnetic permeability, the electric permittivity and the…

Analysis of PDEs · Mathematics 2016-01-20 Pedro Caro , Ting Zhou

In this work, we study the inverse problem of determining a potential coefficient in an abstract wave equation that includes a lower-order term. The equation incorporates a time-fractional derivative in the Caputo sense, as well as a…

Analysis of PDEs · Mathematics 2025-07-10 D. K. Durdiev , H. H. Turdiev , A. A. Rahmonov

The fractional Sturm-Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore to obtain solutions or approximation of solutions…

Numerical Analysis · Mathematics 2016-04-15 Ricardo Almeida , Agnieszka B. Malinowska , M. Luísa Morgado , Tatiana Odzijewicz

We consider initial boundary value problems for time fractional diffusion-wave equations: $$ d_t^{\alpha} u = -Au + \mu(t)f(x) $$ in a bounded domain where $\mu(t)f(x)$ describes a source and $\alpha \in (0,1) \cup (1,2)$, and $-A$ is a…

Analysis of PDEs · Mathematics 2023-08-01 Paola Loreti , Daniela Sforza , Masahiro Yamamoto

In this paper, we consider two linear inverse problems for the time-fractional wave equation, assuming that its right-hand side takes the separable form $f(t)h(x)$, where $t \geq 0$ and $x \in \Omega \subset R^N $. The objective is to…

Analysis of PDEs · Mathematics 2025-03-25 Durdiev Durdimurod Kalandarovich

We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low…

Analysis of PDEs · Mathematics 2020-03-24 William McLean , Kassem Mustapha , Raed Ali , Omar Knio

This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and…

Probability · Mathematics 2016-11-29 Erkan Nane , Mark M. Meerschaert , Palaniappan Vellaisamy

We study an inverse boundary value problem on the determination of principal order coefficients in isotropic nonautonomous heat flows stated as follows; given a medium, and in the absence of heat sources and sinks, can the time-dependent…

Analysis of PDEs · Mathematics 2023-05-10 Ali Feizmohammadi

We study the inverse problem for determining the time-dependent matrix potential appearing in the wave equation. We prove the unique determination of potential from the knowledge of solution measured on a part of the boundary.

Analysis of PDEs · Mathematics 2020-01-24 Rohit Kumar Mishra , Manmohan Vashisth

In this work, we consider a generalization of the nonlinear Langevin equation of fractional orders with boundary value conditions. The existence and uniqueness of solutions are studied by using results of the fixed point theory. Moreover,…

Analysis of PDEs · Mathematics 2020-04-08 Saeed Kosari , Milad Yadollahzadeh , Zehui Shao , Yongsheng Rao

In this article, we study an inverse boundary value problem for the time-dependent convection-diffusion equation. We use the nonlinear Carleman weight to recover the time-dependent convection term and time-dependent density coefficient…

Analysis of PDEs · Mathematics 2024-04-17 Anamika Purohit