Related papers: Well-posedness of initial-boundary value problem f…

We establish the well-posedness of an initial-boundary value problem for a general class of time-fractional, advection-diffusion-reaction equations, allowing space- and time-dependent coefficients as well as initial data that may have low…

We study the well-posedness for initial boundary value problems associated with time fractional diffusion equations with non-homogenous boundary and initial values. We consider both weak and strong solutions for the problems. For weak…

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…

We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on spatial and time variables and the zero Dirichlet boundary condition is…

We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite…

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…

We study the Dirichlet boundary-value problem of steady-state two-sided variable-coefficient conservative space-fractional diffusion equations. We show that the Galerkin weak formulation, which was proved to be coercive and continuous for a…

We study an initial-boundary value problem of variable-order time-fractional diffusion equations in one space dimension. Based on the wellposedness of the proposed model and the smoothing properties of its solutions, which are shown to be…

In this paper, we investigate the well-posedness and the long-time asymptotic behavior for the initial-boundary value problem for multi-term time-fractional diffusion equations, where the time differentiation consists of a finite summation…

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…

In this paper, some initial-boundary-value problems for the time-fractional diffusion equation are first considered in open bounded n-dimensional domains. In particular, the maximum principle well-known for the PDEs of elliptic and…

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…

An initial-boundary value problem for a time-fractional subdiffusion equation with an arbitrary order elliptic differential operator is considered. Uniqueness and existence of the classical solution of the posed problem are proved by the…

In this paper, we discuss initial-boundary value problems for linear diffusion equation with multiple time-fractional derivatives. By means of the Mittag-Leffler function and the eigenfunction expansion, we reduce the problem to an integral…

In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the…

We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…

This paper is concerned with the study of the well-posedeness for the initial boundary value problem to the time-fractional wave equation with acoustic boundary conditions. The problem is considered in a bounded and connected domain $\Omega…

In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and…

Using the Galerkin method, we obtain the unique existence of the weak solution to a time fractional wave problem, and establish some regularity estimates which reveal the singularity structure of the weak solution in time.

In this work, we consider an inverse problem of determining a time dependent coefficient in a fully fractional diffusion equation with a nonlinear source term. The nonlocal initial-boundary value problem refers to the forward model: the…