Numerical Simulations for Fitting Parameters of Linear and Logistic-Type Fractional-, Variable-Order Equations - Comparision of Methods
In the work variable-, fractional-order backward difference of the Grünwald-Letnikov type is presented. The backward difference is used to generate simulated experimental data to which additional noise signal is added. Using prepared data four different algorithms of finding the parameter of the order function (assuming that the general family of the function is known) and constant \(\lambda \) coefficient are compared. The algorithms are: trust region algorithm, particle swarm algorithm, simulated annealing algorithm and genetic algorithm.
KeywordsDifference equations Eigenfunction Fractional variable-order Optimization algorithms
The work was supported by Polish founds of National Science Center, granted on the basis of decision DEC-2016/23/B/ST7/03686.
- 1.Almeida, R., Bastos, N.R.O., Monteiro, M.T.T.: A fractional Malthusian growth model with variable order using an optimization approach. Published online in International Academic Press (2018). https://doi.org/10.19139/soic.v6i1.465
- 6.Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN 1995 - International Conference on Neural Networks, Perth, Australia, vol. 4, pp. 1942–1948 (1995). https://doi.org/10.1109/ICNN.1995.488968
- 8.Mozyrska, D., Wyrwas, M.: Systems with fractional variable-order difference operator of convolution type and its stability. ELEKTRONIKA IR ELEKTROTECHNIKA (2018). https://doi.org/10.5755/j01.eie.24.5.21846
- 12.Yuan, Y.: Nonlinear optimization: trust region algorithms. State Key Laboratory of Scientific and Engineering Computing, Academia Sinica, Beijing (1999)Google Scholar
- 13.Yuan, Y.: A review of trust region algorithms for optimization. State Key Laboratory of Scientific and Engineering Computing, Academia Sinica, Beijing (1999). 10.1.1.45.9964Google Scholar