Inverse Analysis of a Loaded Heat Conduction Equation
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
Umida BaltaevaPraveen Agarwal
India
Bobur Khasanov
Hamrobek Hayitbayev
Florence Hubert
France
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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).
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