Naslov
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]

Autori
Gorska, Katarzyna ; Horzela, Andrzej ; Poganj, Tibor

Izvornik
Zeitschrift fur angewandte mathematik und physik (0044-2275) 70 (2019), 5; 141, 6

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

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

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Fizika

POVEZANOST RADA