Fractional-Order Systems and Fractional-Order Controllers (FOSFOC)

Our FOSFOC team has been given the status of an excellent research team by the Accreditation Committee of the Slovak Republic, as one of only 37 research groups in Slovakia that received such status in the first stage. Later, in the second round of evaluation, the Accreditation Committee gave such status to additional 17 research groups.

Team Members

Awards and Other Forms of Recognition


Selected Books

Selected Journal Papers

  1. Leonenko, N., Podlubny, I.: Monte Carlo method for fractional-order differentiation. Fractional Calculus and Applied Analysis, vol. 25, no. 2, 2022, pp. 346–361. (DOI: 10.1007/s13540-022-00017-3)
  2. Leonenko, N., Podlubny, I. Monte Carlo method for fractional-order differentiation extended to higher orders. Fractional Calculus and Applied Analysis, vol. 25, no. 3, 2022, pp. 841–857. (DOI: 10.1007/s13540-022-00048-w)
  3. Petráš, I. Novel Generalized Low-Pass Filter with Adjustable Parameters of Exponential-Type Forgetting and Its Application to ECG Signal. Sensors, vol. 22, 2022, art. 8740. (DOI: 10.3390/s22228740)
  4. Terpák, J.: General one-dimensional model of the time-fractional diffusion-wave equation in various geometries. Fractional Calculus and Applied Analysis, vol. 26, 2023, pp. 599-618. (DOI: 10.1007/s13540-023-00138-3)
  5. Petráš, I.: Novel Fractional-Order Model Predictive Control: State-Space Approach, IEEE Access, vol. 9, 2021, pp. 92769-92775.
  6. Trymorush, I., Podlubny, I.: Porous functions - II. Fractional Calculus and Applied Analysis, 23(2) 2020, 307-323 (DOI: 10.1515/fca-2020-0015).
  7. Podlubny, I.: Porous functions. Fractional Calculus and Applied Analysis, 22(6), 2019, 1502-1516 (DOI:10.1515/fca-2019-0078).
  8. Petráš, I., Terpák, J.: Fractional Calculus as a Simple Tool for Modeling and Analysis of Long Memory Process in Industry, Mathematics, vol. 7, no. 6, 2019.
  9. Gonzalez, E., Petráš, I., Ortigueira, M.D.: Novel polarization index evaluation formula and fractional-order dynamics in electric motor insulation resistance, Fractional Calculus and Applied Analysis, vol. 21, no. 3, 2018, pp. 613-627.
  10. Dimeas, I., Petráš, I., Psychalinos, C.: New analog implementation technique for fractional-order controller: A DC motor control, AEU - International Journal of Electronics and Communications, vol. 78, 2017, pp. 192-200.
  11. Tepljakov, A., Gonzalez, E. A., Petlenkov, E., Belikov, J., Monje, C. A, Petráš, I.: Incorporation of fractional-order dynamics into an existing PI/PID DC motor control loop, ISA Transactions, vol. 60, 2016, pp. 262-273.
  12. Sierociuk, D., Škovránek, T., Macias, M., Podlubny, I., Petráš, I., Dzielinski, A., Ziubinski, P.: Diffusion process modeling by using fractional-order models, Applied Mathematics and Computation, vol. 257, 2015, pp. 2- 11.
  13. Žecová, M., Terpák, J.: Heat conduction modeling by using fractional-order derivatives, Applied Mathematics and Computation, vol. 257, 2015, pp. 365-373.
  14. Žecová, M., Terpák, J.: Fractional Heat Conduction Models and Thermal Diffusivity Determination, Mathematical Problems in Engineering, vol. 2015, 2015,  Article ID 753936, pp. 1-9.
  15. Sierociuk, D., Podlubny, I., Petráš, I.: Experimental Evidence of Variable-Order Behavior of Ladders and Nested Ladders, IEEE Transactions on Control Systems Technology, vol. 21, no. 2, 2013, pp. 459-466.
  16. Petráš, I., Sierociuk, D.; Podlubny, I.: Identification of parameters of a half-order system, IEEE Transactions on Signal Processing, vol. 60, no.10, 2012, pp. 5561-5566.
  17. Petráš, I.: Tuning and implementation methods for fractional-order controllers, Fractional Calculus and Applied Analysis, vol. 5, no.2, 2012, pp. 282-303.
  18. Škovránek, T., Podlubny, I., Petráš, I.: Modeling of the national economies in state-space: A fractional calculus approach, Economic Modelling, vol. 29, no. 4, 2012, pp. 1322-1327.
  19. Petráš, I.: Chaos in Fractional-order Population Model, International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 22, no. 4, 2012.
  20. Petráš, I., Magin, R.: Simulation of drug uptake in a two compartmental fractional model for a biological system, Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 12, 2011, pp. 4588-4595.
  21. Petráš, I.: An Effective Numerical Method and Its Utilization to Solution of Fractional Models Used in Bioengineering Applications. Advances in Difference Equations, vol. 2011, p. 1-14.
  22. Li Y., Chen YQ, Podlubny I.: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Computers & Mathematics with Applications, Volume 59, Issue 5, March 2010, Pages 1810-1821, doi:10.1016/j.camwa.2009.08.019
  23. Li Y., Chen YQ, Podlubny I.: Mittag–Leffler stability of fractional order nonlinear dynamic systems. Automatica, Volume 45, Issue 8, August 2009, Pages 1965-1969, doi:10.1016/j.automatica.2009.04.003.
  24. Podlubny I., Chechkin A.V., Skovranek T., Chen YQ, Vinagre B.: Matrix approach to discrete fractional calculus II: partial fractional differential equations. Journal of Computational Physics, vol. 228, no. 8, 1 May 2009, pp. 3137-3153, doi:10.1016/ — [Pre-print:]
  25. Chen YQ, Ahn HS, Podlubny I.: Robust stability check of fractional order linear time invariant systems with interval uncertainties. Signal Processing, vol. 86, no. 10, pp.2611-2618, October 2006.
  26. Heymans, N., and Podlubny, I.: Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta, vol. 45, no. 5, June 2006, pp. 765–772 — [Pre-print: math-ph/0512028]
  27. Chen, YQ.; Vinagre, B.M.; and Podlubny, I.: Continued Fraction Expansion Approaches to Discretizing Fractional Order Derivatives—an Expository Review. Nonlinear Dynamics, vol. 38 (December 2004), no. 1–2, pp. 155–170.
  28. Chen, YQ.; Vinagre, B.M.; and Podlubny, I.: Fractional Order Disturbance Observer for Robust Vibration Suppression. Nonlinear Dynamics, vol. 38 (December 2004), no. 1–2, pp. 355–367.
  29. Podlubny, I.: Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation. Fractional Calculus and Applied Analysis, vol. 5, no. 4, 2002, pp. 367–386.
  30. Podlubny, I.: Fractional-Order Systems and PIλDμ -Controllers, IEEE Transactions on Automatic Control, vol. 44, no. 1, January 1999, pp. 208–213.


Awards of Our Students

Miscellaneous Activities