Inverse analysis of a loaded heat conduction equation
https://doi.org/10.17586/2220-8054-2025-16-6-727-736
Abstract
This work considers an inverse problem for a heat conduction equation that includes fractional loaded terms and coefficients varying with spatial coordinates. By reformulating the original equation into a system of equivalent loaded integro-differential equations, we establish sufficient conditions ensuring the existence and uniqueness of the solution. The study focuses on determining the multidimensional kernel associated with the fractional heat conduction operator. The approach is based on the contraction mapping principle and the use of Riemann-Liouville fractional integrals, providing a mathematical framework applicable to diffusion processes with spatial heterogeneity and memory effects.
About the Authors
U. Baltaeva
Urgench State University
Uzbekistan
Uzbekistan
Umida Baltaeva – Department of Applied Mathematics and mathematical physics
Urgench-220100
P. Agarwal
Anand International College of Engineering
India
India
Praveen Agarwal – Department of Mathematics
Jaipur-303012
B. Khasanov
Khorezm Mamun Academy
Uzbekistan
Uzbekistan
Bobur Khasanov – Department of Exact sciences
Khiva
H. Hayitbayev
Mamun university
Uzbekistan
Uzbekistan
Hamrobek Hayitbayev – Department of Accounting and General Professional Sciences
Khiva
F. Hubert
Aix-Marseille Universite
France
France
Florence Hubert – Aix-Marseille Universite
I2M, Marseille
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Review
For citations:
Baltaeva U., Agarwal P., Khasanov B., Hayitbayev H., Hubert F. Inverse analysis of a loaded heat conduction equation. Nanosystems: Physics, Chemistry, Mathematics. 2025;16(6):727-736. https://doi.org/10.17586/2220-8054-2025-16-6-727-736
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