On a Riesz–Feller space fractional backward diffusion problem with a nonlinear source

Optimal results for a time-fractional inverse diffusion problem under the Hölder type source condition

‎In the present paper we consider a time-fractional inverse diffusion problem‎, ‎where data is given at $x=1$ and the solution is required in the interval $0

Data regularization for a backward time-fractional diffusion problem

Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term

In this paper, we propose a finite difference method for the Riesz space fractional diffusion equations with delay and a nonlinear source term on a finite domain. The proposed method combines a time scheme based on the predictor-corrector method and the Crank-Nicolson scheme for the spatial discretization. The corresponding theoretical results including stability and convergence are provided. S...

Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term

and Applied Analysis 3 Baeumer et al. 8, 13 have proved existence and uniqueness of a strong solution for 1.2 using the semigroup theory when f x, t, u is globally Lipschitz continuous. Furthermore, when f x, t, u is locally Lipschitz continuous, existence of a unique strong solution has also been shown by introducing the cut-off function. Finite difference methods have been studied in 14–16 fo...

A study of a Stefan problem governed with space–time fractional derivatives

This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a variable latent-heat (a power function of position). This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained by using the optimal homotopy asymptotic method to find the solu...