Regularization of a sideways problem for a time-fractional diffusion equation with 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

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Data regularization for a backward time-fractional diffusion problem

Regularization methods for unknown source in space fractional diffusion equation

We discuss determining the unknown steady source in a space fractional diffusion equation and show that both the Fourier and avelet dual least squares regularization methods work well for the ill-posed problem. The detailed error estimates are also strictly stablished for both of the methods. Moreover, the algorithm implementation and the corresponding numerical results are presented or the Fou...

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