Analysis of linear continuous-time systems by the use of the conformable fractional calculus and Caputo

• Autorzy: Piotrowska E.

Identyfikatory

DOI

10.24425/123668

• Języki publikacji: EN

Abstrakty

EN

The paper presents general solutions for fractional state-space equations. The analysis of the fractional electrical circuit in the transient state is described by the equation of the state and space equations. The results are presented for the voltage of a capacitor and current in a coil, for different alpha values. The Caputo and conformable fractional derivative definitions have been considered. At the end, the results have been obtained.

Słowa kluczowe

EN

conformable fractional derivative; fractional electrical circuit; different fractional order system

• Wydawca: Polish Academy of Sciences, Committee on Electrical Engineering
• Czasopismo: Archives of Electrical Engineering
• Rocznik: 2018
• Tom: Vol. 67, nr 3
• Strony: 629–--639
• Opis fizyczny: Bibliogr. 14 poz., rys., wz.

Twórcy

autor

Piotrowska E.

• Faculty of Electrical Engineering, Bialystok University of Technology Wiejska 45D, 15-351 Białystok, Poland

Bibliografia

• [1] Abdeljawad T., On conformable fractional calculus, J. Comp. and Appl. Math., vol. 279, pp. 57–66 (2015).
• [2] Alsaedi A., Nieto J.J.,VenkteshV., Fractional electrical circuits,Advances in Mechanical Engineering, vol. 7, no. 12, pp. 1–7 (2015).
• [3] Kaczorek T., Analysis of fractional electrical circuits in transient states, Logistyka, vol. 2 (2010).
• [4] Kaczorek T., Positivity and Reachability of Fractional Electrical Circuits, Acta Mechanica et Automatica, col. 5, no. 2, pp. 42–51 (2011).
• [5] Kaczorek T., Singular fractional linear systems and electrical circuits, Int. J. Appl. Math. Comput. Sci., vol. 21, no. 2, pp. 379–384 (2011).
• [6] Khalil R., Al Horani A., Yousef A., Sababheh M., A new definition of fractional derivative, Journal of Comput. Appl. Math., vol. 264, pp. 65–70 (2014).
• [7] Jesus I.S., Tenreiro Machado J.A., Comparing Integer and Fractional Models in some Electrical Systems, Proc. 4th IFAC Workshop Fractional Differentiation and its Applications, Badajoz, Spain, October 18–20 (2010).
• [8] Caponetto R., Dongola G., Fortuna L., Petráś I., Fractional Order Systems. Modeling and Control Applications, World Scientific (2010).
• [9] Gantmacher F.R., The Theory of Matrices, vol. I and II, Chelasea Publishing Co., New York (1959).
• [10] Kaczorek T., Selected Problems in Fractional Systems Theory, Springer-Verlag, Berlin (2012).
• [11] Kaczorek T., Rogowski K., Fractional Linear Systems and Electrical Circuits, Springer (2014).
• [12] Ostalczyk P., Epitome of Fractional Calculus: Theory and Aplications in Automatics, Lodz Technical University Publishing (in Polish), Lodz 2008, to be published.
• [13] Oldham K.B, Spanier J., The Fractional Calculus, Accademic Press, New York (1974).
• [14] Podlubny I., Fractional Differential Equations, Academic Press, San Diego (1999).

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).