Geodesic
Boundary value problem for a differential-difference equation
News of the Kabardin-Balkar scientific center of RAS, Tome 26 (2024) no. 4, pp. 130-144

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The work is devoted to the study of a differential-difference equation with a fractional derivative of order not exceeding one. For the equation under consideration, a boundary value problem is posed and solved on a manifold that is a countable union of intervals. To solve the problem, we used an analogue of the Green function method, adapted for differential-difference equations. A general representation of the solution to the equation under study has been found, a fundamental solution has been constructed in terms of the Prabhakar function, its properties have been studied, and a theorem on the existence and uniqueness of a solution to the problem under study has been proven.
Keywords: fractional derivative, McKendrick – Von Foerster equation, fractional integration operator, fractional differentiation operator, differential-difference equation, Riemann – Liouville integral, difference operators, Prabhakar function, Mittag-Leffler function 
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L. M. Vidzizheva; D. A. Kanametova. Boundary value problem for a differential-difference equation. News of the Kabardin-Balkar scientific center of RAS, Tome 26 (2024) no. 4, pp. 130-144. http://geodesic.mathdoc.fr/item/IZKAB_2024_26_4_a5/