Three Landweber iterative methods for solving the initial value problem of time-fractional diffusion-wave equation on spherically symmetric domain

The backward problem for radially symmetric time‐fractional diffusion‐wave equation under Robin boundary condition

“…In this paper, we are interested in studying the backward problem of the radially symmetric time‐fractional diffusion‐wave equation. There are only a few papers 9–11 on the inverse problem of the radially symmetric time‐fractional diffusion or diffusion‐wave equation, but these papers are limited to the Dirichlet boundary condition () or the Neumann boundary condition (). $$$$ u\left(r,t\right)=\sigma (t),\kern2em \left(r,t\right)\in \partial D\times \left[0,T\right].$$…”

“…8 In this paper, we are interested in studying the backward problem of the radially symmetric time-fractional diffusion-wave equation. There are only a few papers [9][10][11] on the inverse problem of the radially symmetric time-fractional diffusion or diffusion-wave equation, but these papers are limited to the Dirichlet boundary condition (1.1) or the Neumann boundary condition (1.2).…”

Two regularization methods for identifying the source term of Caputo–Hadamard time‐fractional diffusion equation

“…Compared with the standard Landweber method, the fractional Landweber iterative regularization method reduces the step of the iteration greatly. Yang et al [19] study the initial value problem of the time-fractional diffusion wave equation in spherically symmetric region by three Landweber iterative regularization methods. Yang et al [20] use the fractional Landweber iterative regularization method to identify the source term problem of time-fractional nonhomogeneous diffusion equation with fractional Laplace operator on nonlocal boundary.…”

The backward problem for radially symmetric time-fractional diffusion-wave equation under Robin boundary condition

“…In this paper, we are interested in studying the backward problems of the radially symmetric time-fractional diffusion-wave equation. There are only a few papers [9,10,11] on the inverse problem of the radially symmetric time-fractional diffusion or diffusion-wave equation, but these papers are limited to the Dirichlet boundary condition (1.1) or the Neumann boundary condition (1.2). u(r, t) = σ(t), (r, t) ∈ ∂D × [0, T ].…”