Open AccessA source inverse problem for the pseudo–parabolic equation with the fractional Sturm–Liouville operator
Author(s) -
Daurenbek Serikbaev,
Niyaz Tokmagambetov
Publication year - 2020
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2020m4/143-151
Subject(s) - uniqueness , mathematics , inverse problem , sturm–liouville theory , operator (biology) , inverse , mathematical analysis , fractional calculus , boundary value problem , biochemistry , chemistry , geometry , repressor , transcription factor , gene
A class of inverse problems for restoring the right-hand side of the pseudo-parabolic equation with one fractional Sturm–Liouville operator is considered. In this paper, we prove the existence and uniqueness results of the solutions using by the variable separation method that is to say the Fourier method. We are especially interested in proving the existence and uniqueness of the solutions in the abstract setting of Hilbert spaces. The mentioned results are presented as well as for the Caputo time fractional pseudoparabolic equation. There are many cases in which practical needs lead to problems determining the coefficients or the right side of a differential equation from some available decision data. These are called inverse problems of mathematical physics. Inverse problems arise in various areas of human activity, such as seismology, mineral exploration, biology, medicine, industrial quality control goods, and so on. All these circumstances put the inverse problems among the important problems of modern mathematics.