Geodesic
On a method of solving the Cauchy problem for one-dimensional polywave equation with singular Bessel operator
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 27-41

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We study the Cauchy problem for an equation with singular Bessel operator. Unlike traditional methods to solve this problem, we apply Erdélyi–Kober fractional operator and find an explicit formula for the sought-for solution. We prove that the resulting formula is a unique classical solution to the problem.
Keywords: Cauchy problem, singular Bessel operator, Erdélyi–Kober operator.
Mots-clés : polywave equation 
@article{IVM_2017_8_a2,
     author = {Sh. T. Karimov},
     title = {On a method of solving the {Cauchy} problem for one-dimensional polywave equation with singular {Bessel} operator},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {27--41},
     publisher = {mathdoc},
     number = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_8_a2/}
}
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Sh. T. Karimov. On a method of solving the Cauchy problem for one-dimensional polywave equation with singular Bessel operator. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2017), pp. 27-41. http://geodesic.mathdoc.fr/item/IVM_2017_8_a2/