ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Existence and uniqueness of the solution of a differential equation of fractional diffusion


Alexander Fedorovich Tedeev

PhD in phisics and mathematics
Dept. of functional analysis and differential equations
K. Khetagurov North-Osetian State University
Vatutin str. 44-46,
362025, Vladikaukaz, RSO-A, Russia


In this paper we consider a mixed Dirichlet problem for a linear homogeneous fractional diffusion equation. The existence and uniqueness of the solution of the problem using the harmonic continuation of the solution is proved. As a result, the solution of the differential equation is defined as a trace of a harmonic function. This approach allows us to introduce an integral identity whose solutions are pairs of functions such that the first coordinate of this pair is the desired solution, and the second one is its harmonic continuation. The continuity of the first coordinate in the integral norm is proved as well.



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