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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] (CROSBI ID 268059)

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Gorska, Katarzyna ; Horzela, Andrzej ; Poganj, Tibor 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] // Zeitschrift für angewandte Mathematik und Physik, 70 (2019), 5; 141, 6. doi: 10.1007/s00033-019-1186-z

Podaci o odgovornosti

Gorska, Katarzyna ; Horzela, Andrzej ; Poganj, Tibor

engleski

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]

Inspired by the article "Anomalous relaxation model based on the fractional derivative with a Prabhakar-like kernel" (Z. Angew. Math. Phys. (2019) 70:42) which authors D. Zhao and HG. Sun studied the integro-differential equation with the kernel given by the Prabhakar function $e^{; ; ; - \gamma}; ; ; _{; ; ; \alpha, \beta}; ; ; (t, \lambda)$ we provide the solution to this equation which is complementary to that obtained up to now. Our solution is valid for effective relaxation times which admissible range extends the limits given in \cite[Theorem 3.1]{; ; ; ; DZhao2019}; ; ; ; 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.

Anomalous relaxation ; Colo-Cole model ; Debye relaxation ; Prabhakar function ; Fractional derivative

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Podaci o izdanju

70 (5)

2019.

141

6

objavljeno

0044-2275

1420-9039

10.1007/s00033-019-1186-z

Povezanost rada

Matematika, Fizika

Poveznice
Indeksiranost