Non-homogeneous boundary value problems for fractional diffusion equations in $L^2$-setting

TL;DR

This paper investigates the regularity of solutions to fractional diffusion equations with non-homogeneous boundary conditions using the transposition method in an $L^2$ setting.

Contribution

It provides new insights into the regularity properties of fractional diffusion equations with non-homogeneous boundary data.

Findings

Established regularity results for fractional diffusion equations with non-homogeneous boundary conditions.

Applied the transposition method to analyze boundary value problems in $L^2$-spaces.

Abstract

In the present article, we study the diffusion equations with fractional time derivatives. The aim of this paper is to investigate the best possible regularity for the initial value/boundary value problems with non-homogeneous Dirichlet boundary data. The main tool we use here is called the transposition method.