R. I. Parovik, “The method of Green's function for one differential equation of a fractional order”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 2010, Number 1(1),Pages <nobr>17

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MATHEMATICS

The method of Green's function for one differential equation of a fractional order

R. I. Parovik^ab

^a Institute of Cosmophysical Researches and Radio Wave Propagation Far-Eastern Branch, Russian Academy of Sciences, 684034, Kamchatskiy Kray, Paratunka, Mirnaya st., 7, Russia
^b Branch of Far-Eastern National Technical University, 683031, Petropavlovsk-Kamchatskiy, Tushkanova st. , 11/1, Russia

Abstract: The differential equation of a fractional order $0<\beta<1$ is considered. Green's function for such equation is constructed and is shown that in a case $\beta = 1$ the found decision passes in earlier known classical decision.

Keywords: Green's function, problem of Koshi, Gerasimov-Kaputo operator.

UDC: 517.955

MSC: 35C05

Received: 10.11.2010

DOI: 10.18454/2079-6641-2010-1-1-17-23