Geodesic
The Cauchy problem for the degenerated partial differential equation of the high even order
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 853-862

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In this paper we develop a method for investigating the Cauchy problem for a degenerate differential equation of high even order. Applying the generalized Erdélyi–Kober operator, the formulated problem reduces to a problem for an equation without degeneracy. Further, necessary and sufficient conditions for reducing the order of the equation are proved. Two examples demonstrate the application of the developed method.
Keywords: Fractional integrals and derivatives, generalized Erdélyi–Kober operator, Bessel operator, degenerate differential equations. 
@article{SEMR_2018_15_a94,
     author = {Sh. T. Karimov},
     title = {The {Cauchy} problem for the degenerated partial differential equation of the high even order},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {853--862},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a94/}
}
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Sh. T. Karimov. The Cauchy problem for the degenerated partial differential equation of the high even order. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 853-862. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a94/