Title

Some applications of fractional order calculus

Journal title

Bulletin of the Polish Academy of Sciences Technical Sciences

Yearbook

2010

Volume

58

Issue

No 4

Authors

Dzieliński, A. ; Sierociuk, D. ; Sarwas, G.

Divisions of PAS

Nauki Techniczne

Coverage

583-592

Date

2010

Identifier

DOI: 10.2478/v10175-010-0059-6 ; ISSN 2300-1917

Source

Bulletin of the Polish Academy of Sciences: Technical Sciences; 2010; 58; No 4; 583-592

References

Oldham K. (1974), The Fractional Calculus. ; Podlubny I. (1999), Fractional Differential Equations. ; Stiassnie M. (1979), On the application of fractional calculus for the formulation of viscoelastic models, Applied Mathematical Modelling, 3, 300, doi.org/10.1016/S0307-904X(79)80063-3 ; Bagley R. (1983), Fractional calculus - a different approach to the analysis of viscoelastically damped structures, AIAA J, 21, 741, doi.org/10.2514/3.8142 ; A. Le Méhauté (1991), Fractal Geometries, Theory and Applications. ; Oustaloup A. (1993), Commande CRONE. ; Oustaloup A. (1995), The crone control of resonant plants: Application to a flexible transmission, Eur. J. Control, 1, 113. ; J. Tenreiro Machado (1997), Analysis and design of fractionalorder digital control systems, SAMS-J. Systems Analysis, Modelling, Simulation, 27, 107. ; Vinagre B. (2002), Fractional order systems and fractional order control actions, null, 1. ; Matignon D. (1998), Stability properties for generalized fractional differential systems, ESAIM: Proc., Fractional Differential Systems: Models, Methods and Applications, 5, 145. ; Dorčák L. (2002), Fractional-order state space models, null, 1. ; Barbosa R. (2004), Least-squares design of digital fractional-order operators, null, 1. ; Dzieliński A. (2006), Observer for discrete fractional order state-space systems, null, 1. ; Ostalczyk P. (2008), An Outline of Fractional Advanced Calculus. ; Kaczorek T. (2009), The Chosen Problems of the Theory of Systems of a Non-integral Order. ; Jifeng W. (2005), Frequency domain analysis and applications for fractional-order control systems, J. Physics: Conference Series, 13, 268, doi.org/10.1088/1742-6596/13/1/063 ; Meerschaert M. (2006), Finite difference methods for two-dimensional fractional dispersion equation, J. Computational Physics, 211, 1, 249, doi.org/10.1016/j.jcp.2005.05.017 ; Mikusiński J. (1983), Operational Calculus.