About one inverse problem of time fractional evolution with an involution perturbation

Baurzhan Aibek, Aizat Sh. Aimakhanova, Gani A. Besbaev, Makhmud Abdysametovich Sadybekov

2018

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DOI 10.1063/1.5049006
Data confidence 70 medium
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Abstract

We consider an inverse problem for a one-dimensional fractional evolution equation with involution and with periodic boundary conditions with respect to a space variable. This equation interpolates heat and wave equations. The inverse problem consists in the restoration (simultaneously with the solution) of the unknown right-hand side of the equation, which depends only on the spatial variable. The conditions for redefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.