Comparison of mathematical models with fractional derivative for the heat conduction inverse problem based on the measurements of temperature in porous aluminum

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

“…Mathematical fundaments and results concerning the convergence of the different versions of the ACO algorithm are included in [ 24 , 25 , 26 , 27 ]. Based on the analysis of the papers of various authors, see for example [ 28 , 29 , 30 , 31 , 32 ], as well as on the computation carried out by us (for example [ 7 , 17 , 20 , 22 , 31 ]) we come to the conclusion that using the artificial intelligence algorithms (ACO, RACO, RACO, IRM, etc.) in most cases does not require the application of the explicit regulatory procedures.…”

“…Generally speaking, the solution of the inverse heat conduction problem consists in such a choice of the model parameters (model input) so the given output temperature distribution is obtained. More information regarding the heat processes modeling in the porous materials, inverse heat conduction problems, and use of the fractional calculus for modeling these kind of processes may be found in [ 5 , 7 , 19 , 20 , 21 ].…”

“…Voller [ 5 ] shows that for the materials of anomalous porosity, the models containing the fractional derivative are better for describing the problem that the models with the classical derivative. The experiments conducted in the papers [ 6 , 7 ] show that the fractional derivatives make sense when describing the phenomenon of the heat conduction in such materials as the composites or the porous aluminum. In [ 6 ], the authors consider the inverse heat conduction problem in the composite material.…”

“…For the model presented in this paper the fractional derivative of the Caputo type was used. 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. Moreover, in this case the fractional derivative turned out to be better for describing the phenomenon.…”

Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation

“…In case of the heat conduction problems the equations with the fractional derivatives are particularly useful for modeling the phenomena that take place in the porous materials and composites due to the fact that the anomalous diffusion process occurs there. For such materials the models with the fractional derivatives give better results than the models based on the classic derivatives, as has been shown, for example, in papers [6,7]. In the articles [7,8] the heat conduction process was considered in composites and porous aluminum.…”