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

Authors：Gorska, K^*; Horzela, A; Pogany, T K

Source：Zeitschrift für Angewandte Mathematik und Physik, 2019, 70(5): 141.

DOI：10.1007/s00033-019-1186-z

Inspired by the article "Anomalous relaxation model based on the fractional derivative with a Prabhakar-like kernel" (Z. Angew. Math. Phys. (2019) 70:42) whose authors Zhao and Sun studied the integro-differential equation with the kernel given by the Prabhakar function e(alpha,beta)(-gamma) (t, lambda), we provide the solution to this equation which is complementary to that obtained up to now. Our solution is valid for effective relaxation times whose admissible range extends the limits given in Zhao and Sun (Z Angew Math Phys 70: 42, 2019, Theorem 3.1) to all positive values. For special choices of parameters entering the equation itself and/or characterizing the kernel, the solution comprises to known phenomenological relaxation patterns, e.g., to the Cole-Cole model (if gamma = 1, beta = 1 - alpha) or to the standard Debye relaxation.

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