Related papers: Inverse source problems for a multidimensional tim…
In this paper, we investigate the direct and linear inverse problems of identifying time-dependent and time-independent source terms in a time-fractional diffusion-wave equation, using measured data at an interior point of the time…
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…
In this paper, we study the inverse problem of finding a time-dependent multiplier of the right-hand side of a time-fractional one-dimensional diffusion equation with variables coefficients in the case where the usual Cauchy, homogeneous…
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…
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 $u(0)=u(T)$…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
In the present paper, we investigate the initial-boundary value problem for fractional order parabolic equation on a metric star graph in Sobolev spaces. First, we prove the existence and uniqueness results of strong solutions which are…
In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\alpha\in(0,1)$. Our survey covers the following types of inverse problems: 1.…
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…
In the present paper we consider an inverse source problem for time-fractional mixed parabolic-hyperbolic equation with the Caputo derivative. In case, when hyperbolic part of the considered mixed type equation is wave equation, the…
In this paper, we are concerned with the stochastic time-fractional diffusion-wave equations in a Hilbert space. The main objective of this paper is to establish properties of the stochastic weak solutions of the initial-boundary value…
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…
The paper considers an inverse source problem for a one-dimensional time-fractional heat equation with the generalized impedance boundary condition. The inverse problem is the time dependent source parameter identification together with the…
We consider a fractional diffusion equations of order $\alpha\in(0,1)$ whose source term is singular in time: $(\partial_t^\alpha+A)u(x,t)=\mu(t)f(x)$, $(x,t)\in\Omega\times(0,T)$, where $\mu$ belongs to a Sobolev space of negative order.…
The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse…
This paper investigates an inverse random source problem for stochastic evolution equations, including stochastic heat and wave equations, with the unknown source modeled as $g(x)f(t)\dot{W}(t)$. The research commences with the…
This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…
Inverse problem for multi-term fractional parabolic equation in two dimensional space, involving m + 1 Caputo fractional derivatives in time, is investigated. Presence of nonlocal boundary conditions leads to a non-self-adjoint spectral…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
In this paper, we investigate the inverse problem of determining the right-hand side of a subdiffusion equation with a Caputo time derivative, where the right-hand side depends on both time and certain spatial variables. Similar inverse…