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Zbl 1155.33005
Varlamov, Vladimir
Differential and integral relations involving fractional derivatives of Airy functions and applications. (English)
[J] J. Math. Anal. Appl. 348, No. 1, 101-115 (2008). ISSN 0022-247X

Authors' summary: Various differential and integral relations are deduced that involve fractional derivatives of the Airy function $Ai(x)$ and the Scorer function $Gi(x)$. Several new Wronskian relations are obtained that lead to the calculation of a number of indefinite integrals containing fractional derivatives of the Airy functions. New fractional derivative conservation laws are derived for equations of the Korteweg-de Vries type.
[Juri M. Rappoport (Moskva)]

MSC 2000:: *33C10 Cylinder functions, etc.
26A33 Fractional derivatives and integrals (real functions)
35Q53 KdV-like equations

Keywords: fractional derivatives of Airy functions; integrals; Wronskian relations; fractional derivative conservation laws; equations of Korteweg-de Vries type

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