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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 853–862 (Mi semr960)  

Differentical equations, dynamical systems and optimal control

The Cauchy problem for the degenerated partial differential equation of the high even order

Sh. T. Karimov

Fergana State University, Fergana, Murabbiylar street, 19, 150100, Fergana, Uzbekistan

Abstract: In this paper we develop a method for investigating the Cauchy problem for a degenerate differential equation of high even order. Applying the generalized Erdélyi–Kober operator, the formulated problem reduces to a problem for an equation without degeneracy. Further, necessary and sufficient conditions for reducing the order of the equation are proved. Two examples demonstrate the application of the developed method.

Keywords: Fractional integrals and derivatives, generalized Erdélyi–Kober operator, Bessel operator, degenerate differential equations.

DOI: https://doi.org/10.17377/semi.2018.15.073

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Bibliographic databases:

Document Type: Article
UDC: 517.955
MSC: 35L80
Received February 16, 2018, published August 15, 2018
Language: English

Citation: Sh. T. Karimov, “The Cauchy problem for the degenerated partial differential equation of the high even order”, Sib. Èlektron. Mat. Izv., 15 (2018), 853–862

Citation in format AMSBIB
\Bibitem{Kar18}
\by Sh.~T.~Karimov
\paper The Cauchy problem for the degenerated partial differential equation of the high even order
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 853--862
\mathnet{http://mi.mathnet.ru/semr960}
\crossref{https://doi.org/10.17377/semi.2018.15.073}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000454860200014}


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