Initial-boundary problem for degenerate high order equation with fractional derivative

Abstract

In the article, in a rectangular domain, by the Fourier method, the initial boundary value problem for a high-order equation with two lines of degeneracy with a fractional derivative in the sense of Caputo is investigated for uniqueness and solvability. Sufficient conditions for the well-posedness of the problem posed are obtained.

Boundary value problem for a degenerate equation with a Riemann-Liouville operator

“…As for the degenerate partial differential equations involving fractional derivatives, it should be noted that the researches in this area are quite new. We mention here papers [8][9][10][11][12][13][14][15], in which various boundary value problems for degenerate equations involving fractional derivatives were studied. It should also be noted that fractional-order integro-differential operators have been recently actively used in nanosystem studies.…”