Boundary value problem for a loaded fractional diffusion equation
Pskhu A.V. Ramazanov M.I. Kosmakova M.T.
2023TUBITAK
Turkish Journal of Mathematics
2023#47Issue 51585 - 1594 pp.
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 derivative , Fractional diffusion equation , integral equation , loaded equation , Wright function
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Institute of Applied Mathematics and Automation, Kabardino-Balkarian Scientific Center of RAS, Nalchik, Russian Federation
Buketov Karaganda University, Karaganda, Kazakhstan
Institute of Applied Mathematics and Automation
Buketov Karaganda University
10 лет помогаем публиковать статьи Международный издатель
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