A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem

Abstract

We consider a two-dimensional time fractional diffusion equation and address the important inverse problem consisting of the identification of an ingredient in the source term. The fractional derivative is in the sense of Caputo. The necessary regularization procedure is provided by a two-dimensional discrete mollification operator. Convergence results and illustrative numerical examples are included.

Keywords

• inverse problem
• mollification
• fractional derivatives