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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:
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
26A33 Fractional derivatives and integrals
35Q53 KdV equations (Korteweg-de Vries equations)
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