najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1493Research ArticleMATHEMATICSМАТЕМАТИКАInverse Analysis of a Loaded Heat Conduction Equationhttps://orcid.org/0000-0001-9687-5220BaltaevaUmidaumida_baltayeva@mail.ruhttps://orcid.org/0000-0001-7556-8942AgarwalPraveenumidamath26@gmail.comKhasanovBoburxasanovboburjon.1993@gmail.comHayitbayevHamrobekhamrohayitboyev07@gmail.comHubertFlorencemath.conference2018@gmail.comUrgench State universityUzbekistan2025050220261661493Copyright © Baltaeva U., Agarwal P., Khasanov B., Hayitbayev H., Hubert F., 20262026Baltaeva U., Agarwal P., Khasanov B., Hayitbayev H., Hubert F.Baltaeva U., Agarwal P., Khasanov B., Hayitbayev H., Hubert F.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1493

This work considers an inverseproblem for a heat conduction equation that includes fractionalloaded terms and coefficients varying with spatial coordinates. Byreformulating the original equation into a system of equivalentloaded integro-differential equations, we establish sufficientconditions ensuring the existence and uniqueness of the solution.The study focuses on determining the multidimensional kernelassociated with the fractional heat conduction operator. Theapproach is based on the contraction mapping principle and the useof Riemann-Liouville fractional integrals, providing a mathematicalframework applicable to diffusion processes with spatialheterogeneity and memory effects.

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The authors declare that there are no conflicts of interest present.