This article is cited in 3 papers

Second boundary-value problem in a half-strip for equation of parabolic type with the Bessel operator and Riemann–Liouville derivative

F. G. Khushtova

Institute of Applied Mathematics and Automation, 89A Shortanov str., Nalchik, 360000 Russia

Abstract: 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, parabolic equation, 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.

UDC: 517.95

Received: 02.03.2016

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:7, 73–82

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