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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, Issue 1(34), Pages 134–144 (Mi vsgtu1272)  

Mathematical Modeling

Development of Identification Methods for Fractional Differential Equations with Riemann–Liouville Fractional Derivative

A. S. Ovsienko

Samara State Technical University, Samara, 443100, Russian Federation

Abstract: The methods for parametric identification of fractional differential operators with $\alpha \in (1, 2)$ degree according to instantaneous values of experimental observations based on the Barrett differential equation example are suggested. The methods are based on construction of the linear parametrical discrete model for fractional differential equation. The coefficients of the model are associated with the required parameters of differentiation equation of fractional order. Different approaches to the determination of the relationships between the parameters of the differential equation and the discrete model coefficients are considered. Connection expressions for coefficients of linear parametrical discrete model and Cauchy type problem parameters to be identified are obtained. The algorithm of the method which let us reduce the problem to computation of mean-square estimates for coefficients of linear parametrical discrete model is described. Numerical investigations have been done; furthermore, their results let us conclude high efficiency of the methods.

Keywords: fractional differential operators, parametric identification, linear parametrical discrete model, difference equation

DOI: https://doi.org/10.14498/vsgtu1272

Full text: PDF file (655 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

Document Type: Article
UDC: 517.929.2:517.968.7
MSC: 65P40, 37M05, 26A33
Original article submitted 19/X/2013
revision submitted – 20/XI/2013

Citation: A. S. Ovsienko, “Development of Identification Methods for Fractional Differential Equations with Riemann–Liouville Fractional Derivative”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(34) (2014), 134–144

Citation in format AMSBIB
\Bibitem{Ovs14}
\by A.~S.~Ovsienko
\paper Development of Identification Methods for~Fractional Differential Equations with Riemann--Liouville Fractional Derivative
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2014
\vol 1(34)
\pages 134--144
\mathnet{http://mi.mathnet.ru/vsgtu1272}
\crossref{https://doi.org/10.14498/vsgtu1272}
\zmath{https://zbmath.org/?q=an:06968831}
\elib{http://elibrary.ru/item.asp?id=22813966}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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