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This paper analyzes heat equation with memory in the case of\udkernels that are linear combinations of Gamma distributions. In this case, it is possible to rewrite the non-local equation as a local system of partial differential equations of hyperbolic type. Stability is studied in details by analyzing the corresponding dispersion relation, providing sufficient stability condition for the general case and sharp instability thresholds in the case of linear combination of the first three Gamma functions

Stability analysis for linear heat conduction with memory kernels described by Gamma functions