On time-fractional representation of an open system response-Reference-Cited by-同舟云学术

On time-fractional representation of an open system response

Published:2016-10-01 Issue:5 Volume:19 Page:1306-1315
ISSN:1311-0454
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Uchaikin Vladimir V.¹

Affiliation:

1. Department of Theoretical Physics Ulyanovsk State University 42, Leo Tolstoy Str., Ulyanovsk - 432017, Russian Federation

Abstract

Abstract The article concerns dynamics of an open system (OS) considered as a subsystem of some closed Hamiltonian system. Description of such OS is carried out in terms of integro-differential generalization of the Liouville equation. The Mellin transform allows to present this equation in terms of fractional operators. In frame of these concepts the response problem is formulated and applied to the supercapacitor dynamics. A good agreement with experimental data is found.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2016-0068/pdf

Reference20 articles.

1. N. Bertrand, J. Sabatier, O. Briat, J.-M. Vinassa, Embedded fractional nonlinear supercapacitor model and its parametric estimation method. Industrial Electronics, IEEE Transactions57, No 12 (2010), 3991—4000.

2. A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Y. Gonchar, Distributed order time fractional diffusion equation. Fract. Calc. Appl. Anal6, No 3 (2003), 259—280.

3. M. Di Ventra, Electrical Transport in Nanoscale Systems. Cambridge University Press, New York (2008).

4. A. Dzieliński, G. Sarwas, D. Sierociuk, Comparison and validation of integer and fractional order ultracapacitor models. Advances in Difference Equations2011 No 1 (2011), 15 p.

5. A. Dzieliński, D. Sierociuk, Ultracapacitor modelling and control using discrete fractional order state-space model. Acta Montanistica Slovaca13, No 1 (2008), 136—145.

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