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.
Highlights
The inverse problems are an important and commonly encountered class of problems in many branches of technology and mathematics [1,2]
We consider the model with the fractional differential equation with the fractional derivative [3,4] of the Caputo type
We present the algorithm for solving the inverse problem on the model containing the fractional derivative of the Caputo type
Summary
The inverse problems are an important and commonly encountered class of problems in many branches of technology and mathematics [1,2]. In [7], the authors are comparing the mathematical models containing various derivatives (classical, fractional of the Riemann–Liouville type and fractional of the Caputo type) basing on the experimental data obtained for the porous aluminum. In this case the fractional derivative turned out to be better for describing the phenomenon. We present the algorithm for solving the inverse problem on the model containing the fractional derivative of the Caputo type. The numerical examples used for comparison of the presented algorithm with the algorithm shown in [18] are being presented
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