This article is cited in 8 papers

The Second Boundary-Value Problem in a Half-Strip for a Parabolic-Type Equation with Bessel Operator and Riemann–Liouville Partial Derivative

F. G. Khushtova

Institute of Applied Mathematics and Automation, Nalchik

Abstract: We study the second boundary-value problem in a half-strip for a differential equation with Bessel operator and the Riemann–Liouville partial derivative. In the case of a zero initial condition, a representation of the solution is obtained in terms of the Fox $H$-function. The uniqueness of the solution is proved for the class of functions satisfying an analog of the Tikhonov condition.

Keywords: parabolic-type equation, fractional-order diffusion, Bessel operator, Riemann–Liouville derivative, second boundary-value problem in a half-strip, Fox $H$-function, Tikhonov condition, integral transformation with kernel containing the Wright function.

UDC: 517.95

Received: 20.10.2015
Revised: 15.05.2017

DOI: 10.4213/mzm10986

 English version: Mathematical Notes, 2018, 103:3, 474–482

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