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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.], 2013, Issue 1(30), Pages 245–252 (Mi vsgtu1224)  

This article is cited in 1 scientific paper (total in 1 paper)

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Mechanics and Classical Field Theory

On a class of fractional differential equations for mathematical models of dynamic system with memory

E. N. Ogorodnikov

Samara State Technical University, Samara, 443100, Russia

Abstract: Some differential equation with Riemann–Liouville fractional derivatives is considered. The class of these equations are proposed as a model fractional oscillating equation for the description, analysis and investigation of oscillatory processes in dynamic systems with memory. The obtainment such a kind of equations is based on the hypothesis supposed the existence of the non-ideal viscoelastic connection in the one-dimensional dynamic system, which is associated with the fractional analogy of Zener rheologic model of the viscoelastic body. It's shown, that the initial values problems with Cauchy type conditions is reduced equivalently to the Volterra type integral equations with the differentiable kernels. This circumstance allow to use the method of successive approximation to resolve that integral equations. It's indicated, that such a kind of differential equations may be interesting as mathematical models of nonlinear dynamic systems behavior.

Keywords: differential and integral equations with fractional Riemann–Liouville operators, fractional oscillators, fractional oscillating equations, rheological model of viscoelastic body with memory, Mittag-Leffler type special functions, Volterra type integral equations with special functions in kernel

DOI: https://doi.org/10.14498/vsgtu1224

Full text: PDF file (148 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

Document Type: Article
UDC: 517.925.42
MSC: Primary 34A08; Secondary 26A33, 45K05
Original article submitted 27/I/2013
revision submitted – 17/III/2013

Citation: E. N. Ogorodnikov, “On a class of fractional differential equations for mathematical models of dynamic system with memory”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(30) (2013), 245–252

Citation in format AMSBIB
\Bibitem{Ogo13}
\by E.~N.~Ogorodnikov
\paper On a class of fractional differential equations for~mathematical models of dynamic system with~memory
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2013
\vol 1(30)
\pages 245--252
\mathnet{http://mi.mathnet.ru/vsgtu1224}
\crossref{https://doi.org/10.14498/vsgtu1224}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. N. Ogorodnikov, “Postanovka i reshenie zadachi tipa Koshi dlya odnogo klassa modelnykh dinamicheskikh sistem s pamyatyu”, Trudy devyatoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem. Chast 1, Matematicheskoe modelirovanie i kraevye zadachi, SamGTU, Samara, 2013, 147–152  elib
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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