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Differential and integral relations involving fractional derivatives of Airy functions and applications. (English) Zbl 1155.33005
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.

MSC:
33C10Bessel and Airy functions, cylinder functions, ${}_0F_1$
26A33Fractional derivatives and integrals (real functions)
35Q53KdV-like (Korteweg-de Vries) equations
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References:
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