Related papers: Inverse problem for the abstract diffusion-wave eq…
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…
We present an exponentially convergent numerical method to approximate the solution of the Cauchy problem for the inhomogeneous fractional differential equation with an unbounded operator coefficient and Caputo fractional derivative in…
In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method. This method allows to find exact solutions to nonlinear time-fractional…
An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the…
In this paper we investigate the following fractional order in time Cauchy problem \begin{equation*} \begin{cases} \mathbb{D}_{t}^{\alpha }u(t)+Au(t)=f(u(t)), & 1<\alpha <2, u(0)=u_{0},\,\,\,u^{\prime }(0)=u_{1}. & \end{cases}%…
We consider the determination of an unknown potential $q(x)$ form a fractional diffusion equation subject to overposed lateral boundary data. We show that this data allows recovery of two spectral sequences for the associated inverse…
In this article, we consider a partial differential equation with Caputo time-derivative: $\partial_t^\alpha u + Au = F$ where $0< \alpha < 1$ and $u$ satisfies the zero Dirichlet boundary condition. For a non-symmetric elliptic operator…
In this paper, we investigate direct and inverse source problems for the diffusion equation with two-term generalized fractional derivative (Hilfer derivative) in a rectangular domain. Using spectral expansion method, we derive two-term…
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and…
This paper is concerned with the fractional evolution equation with a discrete distribution of Caputo time-derivatives such that the largest and the smallest orders, $\alpha$ and $\alpha_m$, satisfy the conditions $1<\alpha\le 2$ and…
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…
In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…
We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate the corresponding inverse problems. Our goal is to determine the variable coefficients from the exterior partial measurements of the…
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…
This paper considers the inverse problem of recovering both the unknown, spatially-dependent conductivity $a(x)$ and the potential $q(x)$ in a parabolic equation from overposed data consisting of the value of solution profiles taken at a…
In this paper, we study a time-fractional subdiffusion equation with a nonlinear nonlocal initial condition involving the unknown solution at the final time. The considered problem is formulated using the Caputo fractional derivative of…
We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order $\alpha \in (0,1)$ which are subject to non-zero Neumann boundary conditions. We prove the uniqueness for an inverse…
We study a porous medium equation with right hand side. The operator has nonlocal diffusion effects given by an inverse fractional Laplacian operator. The derivative in time is also fractional of Caputo-type and which takes into account…
This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…
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…