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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 $Ai\left(x\right)$ and the Scorer function $Gi\left(x\right)$. 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, ${}_{0}{F}_{1}$ 26A33 Fractional derivatives and integrals (real functions) 35Q53 KdV-like (Korteweg-de Vries) equations