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We consider the Cauchy problem for stochastic fractional evolution equations with Caputo time fractional derivative of order $1<\alpha<2$ and space variable coefficients on an unbounded domain. The space derivatives that appear in the…

Probability · Mathematics 2025-10-28 Miloš Japundžić , Danijela Rajter-Ćirić

We investigate the inverse problem consisting in the identification of constant coefficients for a fractional-in-time partial differential equation governed by a finite sum of positive self-adjoint operators on a Hilbert space under…

Analysis of PDEs · Mathematics 2025-07-15 Simone Creo , Maria Rosaria Lancia , Andrea Mola , Gianluca Mola , Silvia Romanelli

We consider an inverse problem of reconstructing a degeneracy point in the diffusion coefficient in a one-dimensional parabolic equation by measuring the normal derivative on one side of the domain boundary. We analyze the sensitivity of…

Analysis of PDEs · Mathematics 2023-11-17 Piermarco Cannarsa , Anna Doubova , Masahiro Yamamoto

We study an inverse problem of determining a time-dependent damping coefficient and potential appearing in the wave equation in a compact Riemannian manifold of dimension three or higher. More specifically, we are concerned with the case of…

Analysis of PDEs · Mathematics 2024-07-26 Boya Liu , Teemu Saksala , Lili Yan

Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…

Numerical Analysis · Mathematics 2023-02-01 Zhengqi Zhang , Zhi Zhou

We study an inverse problem for fractional elasticity. In analogy to the classical problem of linear elasticity, we consider the unique recovery of the Lam\'e parameters associated to a linear, isotropic fractional elasticity operator from…

Analysis of PDEs · Mathematics 2022-10-03 Giovanni Covi , Maarten de Hoop , Mikko Salo

We consider a time-space fractional diffusion equation with a variable coefficient and investigate the inverse problem of reconstructing the source term, after regularizing the problem with the quasiboundary value method to mitigate the…

Numerical Analysis · Mathematics 2025-10-21 Asim Ilyas , Muhammad Faisal Khan , Rosita L. Sormani , Giacomo Tento , Stefano Serra-Capizzano

We consider fractional diffusion-wave equations with source term which is represented in a form of a product of a temporal function and a spatial function. We prove the uniqueness for inveres source problem of determining spatially varying…

Analysis of PDEs · Mathematics 2023-01-18 Masahiro Yamamoto

This article deals with the uniqueness in identifying multiple parameters simultaneously in the one-dimensional time-fractional diffusion-wave equation of fractional time-derivative order $\in (0,2)$ with the zero Robin boundary condition.…

Analysis of PDEs · Mathematics 2021-03-16 Xiaohua Jing , Masahiro Yamamoto

We consider the Cauchy problem for a first-order evolution equation with memory in a finite-dimensional Hilbert space when the integral term is related to the time derivative of the solution. The main problems of the approximate solution of…

Numerical Analysis · Mathematics 2021-11-10 Petr N. Vabishchevich

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

We investigate the inverse problem of recovering an initial source for the wave equation with fractional attenuation, motivated by photoacoustic tomography (PAT). The attenuation is modeled by a Caputo fractional derivative of order…

Analysis of PDEs · Mathematics 2025-10-10 Sebastian Acosta , Benjamin Palacios

In this paper, we consider inverse shape problems coming from diffuse optical tomography and inverse scattering. In both problems, our goal is to reconstruct small volume interior regions from measured data on the exterior surface of an…

Analysis of PDEs · Mathematics 2023-02-13 Govanni Granados , Isaac Harris

We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a…

Classical Analysis and ODEs · Mathematics 2016-04-26 Khaled M. Furati , Olaniyi S. Iyiola , Kassem Mustapha

This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order…

Analysis of PDEs · Mathematics 2024-10-23 Xiaohua Jing , Zhiyuan Li , Masahiro Yamamoto

We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…

Numerical Analysis · Mathematics 2021-09-16 Zhengqi Zhang , Zhi Zhou

This article addresses the inverse source problem for a nonlocal heat equation involving the fractional Laplacian. The primary goal is to reconstruct the spatial component of the source term from partial observations of the system's state…

Numerical Analysis · Mathematics 2025-10-17 Galina García , Joaquín Vidal , Sebastián Zamorano

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 obtain explicit expressions for one unknown thermal coefficient (among the conductivity, mass density, specific heat and latent heat of fusion) of a semi-infinite material through the one-phase fractional Lam\'e-Clapeyron-Stefan problem…

Analysis of PDEs · Mathematics 2015-09-15 Domingo Alberto Tarzia

We describe a class of evolution systems of linear partial differential equations with the Caputo-Dzhrbashyan fractional derivative of order $\alpha \in (0,1)$ in the time variable $t$ and the first order derivatives in spatial variables…

Analysis of PDEs · Mathematics 2013-09-10 Anatoly N. Kochubei