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Variable Parameter, Fractional Order, Discrete, Inertial Transfer Function Models Cover

Variable Parameter, Fractional Order, Discrete, Inertial Transfer Function Models

Open Access
|Mar 2026

References

  1. Al-Saidi, N., Natiq, H., Baleanu, D. and Ibrahim, R. (2022). The dynamic and discrete systems of variable fractional order in the sense of the Lozi structure map, AIMS Mathematics 8(1): 733–751.
  2. Bahaa, G. (2017). Fractional optimal control problem for variable-order differential systems, Fractional Calculus and Applied Analysis 20(10): 1447–1470.
  3. Busłowicz, M. and Kaczorek, T. (2009). Simple conditions for practical stability of positive fractional discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 19(2): 263–269, DOI: 10.2478/v10006-009-0022-6.
  4. Byrski, W. (2007). Control and Obervation in Dynamic Systems, AGH University Press, Kraków, (in Polish).
  5. Caponetto, R., Dongola, G., Fortuna, L. and Petras, I. (2010). Fractional order systems: Modeling and control applications, in L.O. Chua (Ed.), World Scientific Series on Nonlinear Science, University of California, Berkeley, pp. 1–178.
  6. Das, S. (2010). Functional Fractional Calculus for System Identyfication and Control, Springer, Berlin.
  7. Garrappa, R., Giusti, A. and Mainardi, F. (2021). Variable-order fractional calculus: A change of perspective, Communications in Nonlinear Science and Numerical Simulation 102(11): 1–23.
  8. Jolic, M. and Konjik, S. (2023). Controllability and observability of linear time-varying fractional systems, Fractional Calculus and Applied Analysis 26(4): 1709–1739.
  9. Kaczorek, T. (2011). Selected Problems of Fractional Systems Theory, Springer, Berlin.
  10. Kaczorek, T. and Rogowski, K. (2014). Fractional Linear Systems and Electrical Circuits, Bialystok University of Technology, Białystok.
  11. Kaczorek, T. and Ruszewski, A. (2024). The Floquet–Lyapunov transformation for fractional discrete-time linear systems with periodic parameters, Archives of Control Sciences 34(1): 83–89.
  12. Kiskinov, H., Milev, M., Petkova, M. and Zahariev, A. (2024). Variable-order fractional linear systems with distributed delays—Existence, uniqueness and integral representation of the solutions, Fractal and Fractional 8(156): 1–18.
  13. Malesza, W., Macias, M. and Sierociuk, D. (2019). Analytical solution of fractional variable order differential equations, Journal of Computational and Applied Mathematics 348(1): 214–236.
  14. Matychyn, I. and Onyshchenko, V. (2021). Time-optimal control of linear fractional systems with variable coefficients, International Journal of Applied Mathematics and Computer Science 31(3): 375–386, DOI: 10.34768/amcs-2021-0025.
  15. Mozyrska, D. and Ostalczyk, P. (2017). Variable, fractional-order oscillation element, in A. Babiarz et al. (Eds), Theory and Applications of Non Integer Order Systems, Lecture Notes in Electrical Engineering, Vol. 407, Springer, Berlin/Heidelberg pp. 65–76.
  16. Mozyrska, D., Wyrwas, M. and Oziablo, P. (2025). Digital PID controllers with fractional variable order techniques and two discrete-time operator variants, Bulletin of The Polish Academy of Sciences: Technical Sciences 73(3): e153831.
  17. Ostalczyk, P. (2010). Stability analysis of a discrete-time system with a variable-, fractional-order controller, Bulletin of the Polish Academy of Scienes: Technical Sciences 58(4): 613–619.
  18. Ostalczyk, P. (2012). Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains, International Journal of Applied Mathematics and Computer Science 22(3): 533–538, DOI: 10.2478/v10006-012-0040-7.
  19. Ostalczyk, P. (2016). Discrete Fractional Calculus: Applications in Control and Image Processing, World Scientific, Singapore.
  20. Ostalczyk, P. and Mozyrska, D. (2017). Variable, fractional order inertial element, in A. Babiarz et al. (Eds), Theory and Applications of Non Integer Order Systems, Lecture Notes in Electrical Engineering, Vol. 407, Springer, Berlin/Heidelberg, pp. 77–89.
  21. Patnaik, S., Hollkamp, J. and Semperlotti, F. (2020). Applications of variable-order fractional operators: A review, Proceedings of the Royal Society A 476(2234): 1–32.
  22. Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego.
  23. Ross, M. and Samko, S. (1993). Integration and differentiation to a variable fractional order, Integral Transforms and Special Functions 1(3): 277–300.
  24. Sierociuk, D. and Macias, M. (2021). Triple estimation of fractional variable order, parameters, and state variables based on the unscented fractional order Kalman filter, Sensors 21(8159): 1–15.
  25. Sivalingam, S. and Govindaraj, V. (2024). Observability of time-varying fractional dynamical systems with Caputo fractional derivative, Mediterranean Journal of Mathematics 21(76), DOI: 10.1007/s00009-024-02615-2.
  26. Sivalingam, S., Vellappandi, M., Govindaraj, V., Alraddadi, I., Alsharif, F. and Hijaz, A. (2024). Controllability of time-varying fractional dynamical systems, Journal of Taibah University for Science 18(1): 1–14.
  27. Tavares, D., Almeida, R. and Torres, D. (2016). Caputo derivatives of fractional variable order: Numerical approximations, Communications in Nonlinear Science and Numerical Simulation 35(1): 69–87.
  28. Valerio, D. and da Costa, J. (2011). Variable-order fractional derivatives and their numerical approximations, Signal Processing 91(3): 470–483.
  29. Vishnukumar, K., Sivalingam, S. and Govindaraj, V. (2024). Controllability of time-varying fractional dynamical systems with distributed delays in control, Physica Scripta 1(1): 2399378.
  30. Wang, B., Liu, J., Alassafi, M., Alsaadi, F., Jahanshahi, H. and Bekiros, S. (2022). Intelligent parameter identification and prediction of variable time fractional derivative and application in a symmetric chaotic financial system, Chaos, Solitons and Fractals 154(1): 111590.
DOI: https://doi.org/10.61822/amcs-2026-0002 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 13 - 22
Submitted on: Jun 4, 2025
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Accepted on: Oct 30, 2025
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Published on: Mar 21, 2026
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2026 Krzysztof Oprzedkiewicz, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.