The aim of this paper is to present a linear viscoelastic model based on Prabhakar fractional operators. In particular, we propose a modification of the classical fractional Maxwell model, in which we replace the Caputo derivative with the Prabhakar one. Furthermore, we also discuss how to recover a formal equivalence between the new model and the known classical models of linear viscoelasticity by means of a suitable choice of the parameters in the Prabhakar derivative. Moreover, we also underline an interesting connection between the theory of Prabhakar fractional integrals and the recently introduced Caputo-Fabrizio differential operator.
Prabhakar-like fractional viscoelasticity / Giusti, Andrea; Colombaro, Ivano. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - STAMPA. - 56:(2018), pp. 138-143. [10.1016/j.cnsns.2017.08.002]
Prabhakar-like fractional viscoelasticity
GIUSTI, ANDREA;COLOMBARO, IVANO
2018
Abstract
The aim of this paper is to present a linear viscoelastic model based on Prabhakar fractional operators. In particular, we propose a modification of the classical fractional Maxwell model, in which we replace the Caputo derivative with the Prabhakar one. Furthermore, we also discuss how to recover a formal equivalence between the new model and the known classical models of linear viscoelasticity by means of a suitable choice of the parameters in the Prabhakar derivative. Moreover, we also underline an interesting connection between the theory of Prabhakar fractional integrals and the recently introduced Caputo-Fabrizio differential operator.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.