On one class of problems for restoring the density of sources of the process of fractional heat conductivity with respect to initial and final temperature

Dina Kusmangazinova, Issabek Orazov, Makhmud Abdysametovich Sadybekov

2018

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DOI 10.1063/1.5049052
Data confidence 70 medium
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Abstract

We consider a class of problems modeling the process of determining the temperature and density of sources in the process of fractional heat conductivity with respect to given initial and finite temperatures. Their mathematical statement leads to inverse problems for a fractional heat equation in which along with solving the equation we have to find an unknown right-hand side depending only on a spatial variable. The fractional Riemann-Liouville derivative is used. Problems with general boundary conditions with respect to a spatial variable that are not strongly regular are investigated. The problem is considered independently of whether a corresponding spectral problem for an operator of multiple differentiation with not strongly regular boundary conditions has the basis property of root functions. The existence and uniqueness of classical solutions to the problem are proved.