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

• Prof. RNDr. Igor Podlubny, DrSc., academician of the Learned Society of Slovakia
  • Google Scholar Citations: QQkfeNkAAAAJ
  • Publons (Web of Science): J-7462-2012
  • Scopus AuthorID: 6602079929


• Prof. Ing. Ivo Petráš, DrSc., academician of the Learned Society of Slovakia
  • Google Scholar Citations: 01msi28AAAAJ
  • Publons (Web of Science): B-1393-2009
  • Scopus AuthorID: 23975184900


• Prof. Ing. Ján Terpák, PhD.
  • Google Scholar Citations: BlBhYRsAAAAJ
  • Publons (Web of Science): A-5629-2013
  • Scopus AuthorID: 6506701642


• Doc. Ing. Tomas Skovranek, PhD.
  • Google Scholar Citations: T-6-Oe4AAAAJ
  • Publons (Web of Science): B-7845-2017
  • Scopus AuthorID: 23098324100

Awards and Other Forms of Recognition

• Prof. RNDr. Igor Podlubny, DrSc.:
  • NEW: Included in "Top 2% scientists in the World" list (2019-2024; updated August 2024)
  • Author of the most highly cited mathematial book in the world during 2012-2022
  • Academician of the Learned Society of Slovakia (elected 2017)
  • ESET Science Award, 2023 - finalist in the category Outstanding Academic in Slovakia
  • ESET Science Award, 2019 - finalist in the category Outstanding Individual contributor to Slovak Science
  • Scientist of the Year in Slovakia (2012)
  • Prize of the Literary Fund of the Slovak Republic for the most frequently cited book in Slovakia (2009) - for the book "Fractional Differential Equations"
  • Prize of the Literary Fund of the Slovak Republic for the third most frequently cited article in Slovakia (2010) - for the article "Fractional-Order Systems and PI^λD^μ-Controllers", IEEE Transactions on Automatic Control, vol. 44, no. 1, January 1999, pp. 208–213
  • Prize of the Literary Fund of the Slovak Republic for the three-year citation impact (2010, 2007, 2004)
  • Excellence in Teaching Award from JSMF – the Union of Slovak Mathematicians and Physicists (2008)
  • Prize of the Rector of the Technical University of Kosice (2004)
  • Werner von Siemens Excellence Award for Research (2002)
  • Cambridge Colleges Hospitality Scheme research fellowship (2000)


• Prof. Ing. Ivo Petráš, DrSc.:
  • NEW: Included in "Top 2% scientists in the World" list (2020-2024; updated August 2024)
  • Academician of the Learned Society of Slovakia (elected 2019)
  • Award of Ministry of Education of Slovak Republic for science and research in 2020 (main category)
  • Golden Medal of the Association of Slovak Scientific and Technological Societies (Zväz slovenských vedeckotechnických spoločností) in 2020
  • Prize of the Literary Fund of the Slovak Republic for the for the three-year citation impact (2014-2016) – 1st place
  • Prize of the Literary Fund of the Slovak Republic for the third most frequently cited book in Slovakia (2016) - for the book Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, 2011, ISBN 978-3-642-18100-9
  • Silver Medal of the Association of Slovak Scientific and Technological Societies (Zväz slovenských vedeckotechnických spoločností) in 2016
  • Publication of the computational result (chaotic attractor) on the journal cover „Design Issue“, vol. 28, no. 2, 2012, MIT Press (2012)
  • Second place in TOP PAPERS FOR SLOVAKIA IN ENGINEERING – Thomson Reuters, article: Analogue Realizations of Fractional-Order Controllers (2012)
  • Prize of the Literary Fund of the Slovak Republic for the scientific literature (2010) – for the book "Fractional Order Systems: Modeling and Control Applications", World Scientific Publishing, 2010
  • Award of Ministry of Education of Slovak Republic for science and research in 2005 (category: young scientists under 35)
  • Prize of the Literary Fund of the Slovak Republic for the third most frequently cited article in Slovakia (2010) - for the article "Analogue Realizations of Fractional-order Controllers", Nonlinear Dynamics, vol. 29, no. 1–4, 2002, pp. 281–296


• Prof. Ing. Ján Terpák, PhD.
  • Gold Medal of the Association of Slovak Scientific and Technological Societies (Zväz slovenských vedeckotechnických spoločností) in 2017
  • Silver Medal of the Association of Slovak Scientific and Technological Societies (Zväz slovenských vedeckotechnických spoločností) in 2013
  • Gold Medal of the Dean of the BERG Faculty of the Technical University of Košice in 2012
  • "Propagator of Science and Technology" Award of the Association of Slovak Scientific and Technical Societies (Zväz slovenských vedeckotechnických spoločností) in 2007


• Doc. Ing. Tomas Skovranek, PhD.:
  • Student of the Year in Slovak Republic (academic year 2008/2009)

Media

• Video
  • Mathematics and Art. Igor Podlubny speaks about his research and art outputs. RTVS - Radio and Television of Slovakia. Broadcast on October 4, 2023.
  • Igor Podlubny's profile as the finalist of ESET Science Award, 2018
  • Why study technology? - a video about us made by the Slovak Centre for Scientific and Technical Information, 2015
  On evaluation of scientific performance. Igor Podlubny's lecture at Comenius University in Bratislava, November 2015
  • Igor Podlubny's interview (in Slovak) to the nation-wide TV channel TA3, after receiving the Scientist of the Year 2012 award.


• Press (international)
  • Niels Henrik Abel får enda en fjær i hatten (Niels Henrik Abel gets another feather in his cap) -- about the discovery in the history of mathematics made by Igor Podlubny, Richard Magin, and Iryna Trymorush of the earlier works of Niels Henrik Abel in the fractional calculus. (translation to English)
  • Dilemas de alto impacto. La Nacion, May 3, 2006 – an article in the major argentinian newspaper about Igor Podlubny's discovery of the law of constant rations of numbers of citation in different fields of science. (translation to English).


• Press (Slovak)
  • Osobnosti ocenené v súťaži Vedec roka SR 2012.
  • Igor Podlubný (profil finalistu vedeckého ocenenia ESET Science Award)
  • Slovenský výpočet je na titulke prestížneho časopisu

Selected Books

• Monographs
  • Podlubny, I.: Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications. Academic Press, San Diego-Boston-New York-London-Tokyo-Toronto, 1999, 368 pages, ISBN 0125588402.
  • Jiao Zh., Chen YQ, Podlubny I.: Distributed-Order Dynamic Systems: Stability, Simulation, Applications and Perspectives. Springer, London, 2012, ISBN 978-1-4471-2851-9.
  • Petráš, I.: Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, Series: Nonlinear Physical Science, 2011, ISBN 978-3-642-18100-9.
  • Petráš, I.: Fractional Order Systems: Modeling and Control Applications, World Scientific, Series on Nonlinear Science, 2010, ISBN 978-9-814-30419-1.


• Edited volumes
  • Petráš, I. (Editor): Handbook of Fractional Calculus with Applications: Vol.6 Applications in Control, De Gruyter, 2019, ISBN 978-3-11-057174-5.
  • Petráš, I. (Editor): Fractional Order Systems, MDPI, 2019, ISBN 978-3-03921-608-6.

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/j.jcp.2009.01.014 — [Pre-print: http://arxiv.org/abs/0811.1355]
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.

Software

• Ivo Petráš (top 1.5% of Mathworks contributors; rank 265 of 18718; 51493 total downloads to May 9, 2023)
  • https://www.mathworks.com/matlabcentral/profile/authors/870605


• Igor Podlubny (top 3% of Mathworks contributors; rank 573 of 18718; 27489 total downloads to May 9, 2023)
  • https://www.mathworks.com/matlabcentral/profile/authors/869567


• Ján Terpák -
  • https://www.mathworks.com/matlabcentral/profile/authors/566089
  • https://www.mathworks.com/matlabcentral/profile/authors/4491433 (with Monika Žecová)


• Tomas Skovranek -
  • https://www.mathworks.com/matlabcentral/profile/authors/17164126
  • https://www.mathworks.com/matlabcentral/profile/authors/1031042( with Vladimir Despotovic)

Awards of Our Students

• Student of the Year in Slovak Republic
  • Michal Takáč (2020-2021), graduate student of Prof. Ivo Petráš
  • Ján Kukurugya (2010-2011), graduate student of Prof. Ján Terpák
  • Tomáš Škovránek (2008-2009), graduate student of Prof. Igor Podlubny
  • Gabriel Zahorčák (2007-2008), graduate student of Prof. Ivo Petráš


• Falling Walls Lab Slovakia
  • Martin Muzelák – 2st place, 2022; master student of Doc. Ing. Tomas Skovranek
  • Michal Takáč – 1st place, 2020; graduate student of Prof. Ivo Petráš
  • Matej Mikulszky – 3rd place, 2018; master student of Prof. Igor Podlubny (co-advisor).

Miscellaneous Activities

• Igor Podlubny's art exhibition: "Computer-generated and Human-interpreted". University Science Park, Kosice, from November 11, 2021 to February 28, 2022. (Translation to English)
• Výtvarné umenie: Algoritmické vizualizácie pána profesora Igora Podlubného vo forme grafických výstupov generovaných počítačom. SME Blog, April 19, 2022. ( Translation to English)