This article is cited in 3 papers

PHYSICAL-MATHEMATICAL SCIENCES

A problem in the half-strip for fourth order parabolic equation with time fractional Riemann–Liouville derivative

L. L. Karasheva

Institute of Applied Mathematics and Automation – branch of the FSBSE "Federal Scientific Center "Kabardin-Balkar Scientific Center of the Russian Academy of Sciences", 360000, KBR, Nalchik, Shortanov street, 89 A

Abstract: In this work a fourth-order inhomogeneous parabolic equation with time fractional derivative is considered. The fractional derivative is understood in the sense of the Riemann–Liouville derivative. The boundary-value problem in the half-strip for equation under consideration is studied. The linearity of the problem allows reducing it to the solution of a homogeneous fourth order parabolic equation with a fractional derivative with respect to the time variable with a homogeneous initial condition and inhomogeneous boundary conditions. In this paper a fundamental solution for fourth-order parabolic equation with time fractional derivative in terms of the Wright function is presented, а representation of the solution of the problem is constructed and uniqueness of the solution in the class of fast growth functions is proved.

Keywords: Riemann–Liouville fractional derivative, fourth order parabolic equation, problem in the half-strip.

UDC: 517.95

Received: 15.10.2019

DOI: 10.35330/1991-6639-2019-5-91-21-29

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