Related papers: Uniqueness of inverse source problems for time-fra…
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…
We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ can be…
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…
The paper considers the initial-boundary value problem for equation $D^\rho_t u(x,t)+ (-\Delta)^\sigma u(x,t)=0$, $\rho\in (0,1)$, $\sigma>0$, in an N-dimensional domain $\Omega$ with a homogeneous Dirichlet condition. The fractional…
In this paper, we investigate the uniqueness of the phase retrieval problem for the fractional Fourier transform (FrFT) of variable order. This problem occurs naturally in optics and quantum physics. More precisely, we show that if $u$ and…
We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain $\Omega$ over a time interval $(0,T)$, which governs the water density $u(x,t)$ and the vegetation biomass density $v(x,t)$ for $x\in\Omega$ and…
In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of one-dimensional reaction-diffusion equations. Such reaction-diffusion equations include the classical model of…
Inverse problems of recovering space-dependent parameters, e.g., initial condition, space-dependent source or potential coefficient, in a subdiffusion model from the terminal observation have been extensively studied in recent years.…
In this paper, a diffusion operator including conformable fractional derivatives of order {\alpha} ({\alpha} in (0,1)) is considered. The asymptotics of the eigenvalues, eigenfunctions and nodal points of the operator are obtained.…
We consider a solution $u(\cdot,t)$ to an initial boundary value problem for time-fractional diffusion-wave equation with the order $\alpha \in (0,2) \setminus \{ 1\}$ where $t$ is a time variable. We first prove that a suitable norm of…
This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and…
In the present work, we discuss the existence of a unique positive solution of a boundary value problem for nonlinear fractional order equation with singularity. Precisely, order of equation $D_{0+}^\alpha u(t)=f(t,u(t))$ belongs to $(3,4]$…
A class of inverse problems for restoring the right-hand side of a parabolic equation for a large class of positive operators with discrete spectrum is considered. The results on existence and uniqueness of solutions of these problems as…
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…
In this work, we investigate an inverse problem of recovering multiple orders in a time-fractional diffusion model from the data observed at one single point on the boundary. We prove the unique recovery of the orders together with their…
As the most significant difference from parabolic equations, long-time or short-time behavior of solutions to time-fractional evolution equations is dominated by the fractional orders, whose unique determination has been frequently…
In this paper, we consider a diffusion equation with fractional-time derivative with nonsingular Mittag-Leffler kernel in Hilbert spaces. Existence and uniqueness of solution are proved by means of a spectral argument. The existence of…
In this work, forward and inverse problems for a time-fractional pseudo-parabolic equation $D_t^{\rho} [u(t) + \mu Au(t)] + \sigma(t) Au(t) = r(t)g$ are investigated in a Hilbert space, where $A$ is an unbounded, positive, self-adjoint…
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 show that the parabolic equation $u_t + (-\Delta)^s u = q(x) |u|^{\alpha-1} u$ posed in a time-space cylinder $(0,T) \times \mathbb{R}^N$ and coupled with zero initial condition and zero nonlocal Dirichlet condition in $(0,T) \times…