The Numerical Solution of Fractional Diffusion Equation by Using Local Polynomial Regression

Abstract

In this paper, we apply the local polynomial regression for the solution of the one-dimensional fractional diffusion equation. The Caputo fractional derivative is used for the formulation. A numerical example is given to show the application of the present method. The effect of the fractional order (a) of the equation is illustrated by changing a from 1.01 to 1.99.