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Inspired by the article "Anomalous relaxation model based on the fractionalderivative with a Prabhakar-like kernel" (Z. Angew. Math. Phys. (2019) 70:42)which authors D. Zhao and HG. Sun studied the integro-differential equationwith the kernel given by the Prabhakar function $e^{-\gamma}_{\alpha, \beta}(t,\lambda)$ we provide the solution to this equation which is complementary tothat obtained up to now. Our solution is valid for effective relaxation timeswhich admissible range extends the limits given in \cite[Theorem3.1]{DZhao2019} to all positive values. For special choices of parametersentering the equation itself and/or characterizing the kernel the solutioncomprises to known phenomenological relaxation patterns, e.g. to the Cole-Colemodel (if $\gamma = 1, \beta=1-\alpha$) or to the standard Debye relaxation.

A note on paper "Anomalous relaxation model based on the fractional derivative with a Prabhakarlike kernel" [Z. Angew. Math. Phys. (2019) 70:42]