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Reports of AIAS, 2021 Volume 21, Issue 3, Pages 6–15 (Mi aman9)

MATHEMATICS

On a boundary value problem in a half-strip for a fourth-order parabolic equation with a Riemann-Liouville operator in a time variable

L. L. Karasheva

Institute of Applied Mathematics and Automation, Nalchik

Abstract: In this work a fourth-order inhomogeneous parabolic equation with time fractional derivative is considered. The boundary-value problem in the half-strip for equation under consideration is studied. 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

DOI: 10.47928/1726-9946-2021-21-3-6-15



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© Steklov Math. Inst. of RAS, 2025