Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Rafał Brociek; Agata Chmielowska; Damian Słota

doi:10.3390/e22050555

Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Entropy (Basel). 2020 May 15;22(5):555. doi: 10.3390/e22050555.

Authors

Rafał Brociek¹, Agata Chmielowska¹, Damian Słota¹

Affiliation

¹ Department of Mathematics Applications and Methods for Artificial Intelligence, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland.

Abstract

This paper presents the algorithms for solving the inverse problems on models with the fractional derivative. The presented algorithm is based on the Real Ant Colony Optimization algorithm. In this paper, the examples of the algorithm application for the inverse heat conduction problem on the model with the fractional derivative of the Caputo type is also presented. Based on those examples, the authors are comparing the proposed algorithm with the iteration method presented in the paper: Zhang, Z. An undetermined coefficient problem for a fractional diffusion equation. Inverse Probl. 2016, 32.

Keywords: fractional derivative; fractional differential equation; heat conduction; inverse problem; mathematical modeling.