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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]


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 fur angewandte mathematik und physik (2019) (znanstveni, prihvaćen)


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

Vrsta, podvrsta
Radovi u časopisima, znanstveni

Izvornik
Zeitschrift fur angewandte mathematik und physik (2019)

Status rada
Prihvaćen

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



POVEZANOST RADA


Ustanove
Pomorski fakultet, Rijeka

Autor s matičnim brojem:
Tibor Poganj, (159666)

Časopis indeksira:


  • Current Contents Connect (CCC)
  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus