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Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, Number 3(23), Pages 48–56 (Mi vkam254)  

FRACTIONAL CALCULUS AND ITS APPLICATION

Cauchy problem for ordinary differential equation with discretely distributed fractional differentiation operator

L. Kh. Gadzova

Institute of Applied Mathematics and Automation, 360000, Nalchik, Shortanova st., 89A, Russia

Abstract: We consider an initial value problem for ordinary differential equation with discretely distributed fractional differentiation operator. We give the Lagrange formula, prove the existence and uniqueness theorem and construct an explicit form of solution.

Keywords: fundamental solution, Cauchy problem, fractional differentiation operator, Caputo derivative.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00462-
This work was financially supported by the Russian Foundation for Basic Research (project No. 16-01-00462-A).


DOI: https://doi.org/10.18454/2079-6641-2018-23-3-48-56

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Full text: http:/.../gadzova-2018323
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UDC: 517.91
MSC: 34L99
Received: 08.06.2018

Citation: L. Kh. Gadzova, “Cauchy problem for ordinary differential equation with discretely distributed fractional differentiation operator”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2018, no. 3(23), 48–56

Citation in format AMSBIB
\Bibitem{Gad18}
\by L.~Kh.~Gadzova
\paper Cauchy problem for ordinary differential equation with discretely distributed fractional differentiation operator
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2018
\issue 3(23)
\pages 48--56
\mathnet{http://mi.mathnet.ru/vkam254}
\crossref{https://doi.org/10.18454/2079-6641-2018-23-3-48-56}
\elib{http://elibrary.ru/item.asp?id=35604469}


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