Heat conduction modeling by using fractional-order derivatives

Abstract

The article deals with the heat conduction modeling. A brief historical overview of the authors who have dealt with the heat conduction and overview of solving methods is listed in the introduction of article. In the next section a mathematical model of one-dimensional heat conduction with using derivatives of integer- and fractional-order is described. The methods of solving models of heat conduction are described, namely analytical and numerical methods. In the case of numerical methods regards the finite difference method by using Grünwald–Letnikov definition for the fractional time derivative. Implementation of these individual methods was realized in MATLAB. The two libraries of m-functions for the heat conduction model have been created, namely Heat Conduction Toolbox and Fractional Heat Conduction Toolbox. At the conclusion of the article the simulations examples with using toolboxes are listed.