Inverse analysis of a loaded heat conduction equation

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.