Solutions of Time-Fractional Diffusion Equation with Reflecting and Absorbing Boundary Conditions Using Matlab

Abstract

The main objective of this work is to develop Matlab program for solving time-fractional diffusion equation (TFDE) with reflecting and absorbing boundary conditions on finite and infinite domains. Essentially, there are two major codes one for finding the exact solution of the TFDE and other for finding the numerical solu-tion of the TFDE. The code for finding the exact solutions is based on the solutions techniques given in Metzler and Klafter (2000), whereas the code for finding the numerical solutions is based on the explicit and implicit finite difference schemes given by Yuste and Acedo (2005) and Langlands and Henry (2005) respectively. Finally, we illustrate the effectiveness of the codes by applying them to TFDEs with sharp initial data and for various reflecting and absorbing conditions both on finite and infinite domains. The results show the difference of solutions between the stan-dard diffusion equation and the time-fractional diffusion equation.