In this paper we consider a boundary value problem for a loaded fractional diffusion equation. The loaded term has the form of the Riemann-Liouville fractional derivative or integral. The BVP is considered in the open right upper quadrant. The problem is reduced to an integral equation that, in some cases, belongs to the pseudo-Volterra type, and its solvability depends on the order of differentiation in the loaded term and the behavior of the support line of the load in a neighborhood of the origin. All these cases are considered. In particular, we establish sufficient conditions for the unique solvability of the problem. Moreover, we give an example showing that violation of these conditions can lead to nonuniqueness of the solution.
Fractional diffusion equation, loaded equation, fractional derivative, integral equation, Wright function
PSKHU, ARSEN V.; RAMAZANOV, MURAT I.; and KOSMAKOVA, MINZILYA
"Boundary value problem for a loaded fractional diffusion equation,"
Turkish Journal of Mathematics: Vol. 47:
5, Article 21.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss5/21