Geodesic
Second boundary-value problem in a half-strip for equation of parabolic type with the Bessel operator and Riemann--Liouville derivative
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2017), pp. 84-93

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We investigate the second boundary-value problem in the half-strip for parabolic equation with the Bessel operator and Riemann–Liouville partial derivative. In terms of the integral transform with Wright function in the kernel, we find the representation of a solution in the case of zero edge condition. We prove the uniqueness of a solution in the class of functions satisfying an analog of the Tikhonov condition.
Keywords: differential equation with partial derivatives, Bessel operator, modified Bessel function, fractional order derivative, Riemann–Liouville operator, Fox function, Wright function, integral transform with Wright function in kernel, uniqueness of solution, Tikhonov condition.
Mots-clés : parabolic equation 
@article{IVM_2017_7_a9,
     author = {F. G. Khushtova},
     title = {Second boundary-value problem in a half-strip for equation of parabolic type with the {Bessel} operator and {Riemann--Liouville} derivative},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {84--93},
     publisher = {mathdoc},
     number = {7},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_7_a9/}
}
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F. G. Khushtova. Second boundary-value problem in a half-strip for equation of parabolic type with the Bessel operator and Riemann--Liouville derivative. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2017), pp. 84-93. http://geodesic.mathdoc.fr/item/IVM_2017_7_a9/