Related papers: Existence and uniqueness of time-fractional diffus…

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 article deals with time-fractional diffusion equations with time-dependent singular source term. Whenever the order of the time-fractional derivative is either multi-term, distributed or space-dependent, we prove that the system admits…

This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…

We develop a theory of existence and uniqueness for the following porous medium equation with fractional diffusion, $$ \{ll} \dfrac{\partial u}{\partial t} + (-\Delta)^{\sigma/2} (|u|^{m-1}u)=0, & \qquad x\in\mathbb{R}^N,\; t>0, [8pt]…

This study addresses the inverse source problem for the fractional diffusion-wave equation, characterized by a source comprising spatial and temporal components. The investigation is primarily concerned with practical scenarios where data…

This paper explores the forward and inverse problems for a fractional subdiffusion equation characterized by time-dependent diffusion and reaction coefficients. Initially, the forward problem is examined, and its unique solvability is…

We consider the well-posedness of the initial-boundary value problem for a time-fractional partial differential equation with the fractional order lying in (1,2]. For the case of time-dependent coefficients, it is difficult to give an…

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…

In this work we investigate Cauchy problem and initial boundary value problem for time-fractional Airy equation on the graphs with infinite and finite bonds. We studied properties of potentials for this equation and using these properties…

In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…

An inverse problem to determine a space-dependent factor in a semilinear time-fractional diffusion equation is considered. Additional data are given in the form of an integral with the Borel measure over the time. Uniqueness of the solution…

We derive some regularity estimates of the solution to a time fractional diffusion equation, that are useful for numerical analysis, and partially unravel the singularity structure of the solution with respect to the time variable.

In this paper, we obtain the sharp uniqueness for an inverse $x$-source problem for a one-dimensional time-fractional diffusion equation with a zeroth-order term by the minimum possible lateral Cauchy data. The key ingredient is the unique…

In this paper, a new type of the discrete fractional Gr{\"o}nwall inequality is developed, which is applied to analyze the stability and convergence of a Galerkin spectral method for a linear time-fractional subdiffusion equation. Based on…

This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typically studied using regularization methods due to their…

This paper is concerned with the mathematical analysis of the inverse random source problem for the time fractional diffusion equation, where the source is assumed to be driven by a fractional Brownian motion. Given the random source, the…

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 paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic…

We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…

This paper deals with an inverse source problem for the $1$D time-fractional diffusion equation by using boundary measurement. The conditional stability in identification of the unknown source term is proved on the basis of the Fourier…