Boundary value problem for fractional diffusion equation in a curvilinear angle domain
A Pskhu, M.I. Ramazanov, N.K. Gulmanov, S.A. Iskakov
Abstract
We consider a boundary value problem for the fractional diffusion equation in an angle domain with a curvilinear boundary. Existence and uniqueness theorems for solutions are proved. It is shown that Holder continuity of the curvilinear boundary ensures the existence of solutions. The uniqueness is proved in the class of functions that vanish at infinity with a power weight. The solution to the problem is constructed explicitly in terms of the solution of the Volterra integral equation.
Topics & Concepts
Curvilinear coordinatesUniquenessMathematicsMathematical analysisBoundary value problemDomain (mathematical analysis)Volterra integral equationIntegral equationGeometryFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems