Title

Fractional order, discrete model of heat transfer process using time and spatial Grünwald-Letnikov operator

Journal title

Bulletin of the Polish Academy of Sciences Technical Sciences

Yearbook

2021

Volume

69

Issue

No. 1

Affiliation

Oprzędkiewicz, Krzysztof : AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Kraków, Poland

Authors

Oprzędkiewicz, Krzysztof

Keywords

fractional order systems ; heat transfer equation ; fractional order state equation ; Fractional Order Backward Difference ; Grünwald-Letnikov operator ; practical stability

Divisions of PAS

Nauki Techniczne

Coverage

e135843

Bibliography

1.  S. Das, Functional Fractional Calculus for System Identification and Controls, Springer, Berlin, 2010.
2.  R. Caponetto, G. Dongola, L. Fortuna, and I. Petras, “Fractional order systems: Modeling and Control Applications”, in World Scientific Series on Nonlinear Science, ed. L.O. Chua, pp. 1–178, University of California, Berkeley, 2010.
3.  A. Dzieliński, D. Sierociuk, and G. Sarwas, “Some applications of fractional order calculus”, Bull. Pol. Ac.: Tech. 58(4), 583– 592 (2010).
4.  C.G. Gal and M. Warma, “Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions”, Evol. Equ. Control Theory 5(1), 61–103 (2016).
5.  E. Popescu, “On the fractional Cauchy problem associated with a feller semigroup”, Math. Rep. 12(2), 81–188 (2010).
6.  D. Sierociuk et al., “Diffusion process modeling by using fractional-order models”, Appl. Math. Comput. 257(1), 2–11 (2015).
7.  J.F. Gómez, L. Torres, and R.F. Escobar (eds.), “Fractional derivatives with Mittag-Leffler kernel trends and applications in science and engineering”, in Studies in Systems, Decision and Control, vol. 194, ed. J. Kacprzyk, pp. 1–339. Springer, Switzerland, 2019.
8.  M. Dlugosz and P. Skruch, “The application of fractional-order models for thermal process modelling inside buildings”, J. Build Phys. 1(1), 1–13 (2015).
9.  A. Obrączka, Control of heat processes with the use of noninteger models. PhD thesis, AGH University, Krakow, Poland, 2014.
10.  A. Rauh, L. Senkel, H. Aschemann, V.V. Saurin, and G.V. Kostin, “An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems”, Int. J. Appl. Math. Comput. Sci. 26(1), 15–30 (2016).
11.  T. Kaczorek, “Singular fractional linear systems and electri cal circuits”, Int. J. Appl. Math. Comput. Sci. 21(2), 379–384 (2011).
12.  T. Kaczorek and K. Rogowski, Fractional Linear Systems and Electrical Circuits, Bialystok University of Technology, Bialystok, 2014.
13.  I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
14.  B. Bandyopadhyay and S. Kamal, “Solution, stability and realization of fractional order differential equation”, in Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach, Lecture Notes in Electrical Engineering 317, pp. 55–90, Springer, Switzerland, 2015.
15.  D. Mozyrska, E. Girejko, M. Wyrwas, “Comparison of hdifference fractional operators”, in Advances in the Theory and Applications of Non- integer Order Systems, eds. W. Mitkowski et al., pp. 1–178. Springer, Switzerland, 2013.
16.  P. Ostalczyk, “Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains”, Int. J. Appl. Math. Comput. Sci. 22(3), 533–538 (2012).
17.  E.F. Anley and Z. Zheng, “Finite difference approximation method for a space fractional convection–diffusion equation with variable coefficients”, Symmetry 12(485), 1–19 (2020).
18.  P. Ostalczyk, Discrete Fractional Calculus. Applications in Control and Image Processing, World Scientific, New Jersey, London, Singapore, 2016.
19.  M. Buslowicz and T. Kaczorek, “Simple conditions for practical stability of positive fractional discrete-time linear systems”, Int. J. Appl. Math. Comput. Sci. 19(2), 263–269 (2009).
20.  R. Brociek and D. Słota, “Implicit finite difference method for the space fractional heat conduction equation with the mixed boundary condition”, Silesian J. Pure Appl. Math. 6(1), 125–136 (2016).
21.  D. Mozyrska and E. Pawluszewicz, “Fractional discrete-time linear control systems with initialization”, Int. J. Control 1(1), 1–7 (2011).
22.  K. Oprzędkiewicz, “The interval parabolic system”, Arch. Control Sci. 13(4), 415–430 (2003).
23.  K. Oprzędkiewicz, “A controllability problem for a class of uncertain parameters linear dynamic systems”, Arch. Control Sci. 14(1), 85–100 (2004).
24.  K. Oprzędkiewicz, “An observability problem for a class of uncertain-parameter linear dynamic systems”, Int. J. Appl. Math. Comput. Sci. 15(3), 331–338 (2005).
25.  A. Dzieliński and D. Sierociuk, “Stability of discrete fractional order state-space systems”, in Proc. of the 2nd IFAC Workshop on Fractional Differentiation and its Applications, Porto, Portugal, 2006, pp. 505–510.

Date

10.02.21

Type

Article

Identifier

DOI: 10.24425/bpasts.2021.135843

Source

Bulletin of the Polish Academy of Sciences: Technical Sciences; 2021; 69; No. 1; e135843