Fractional integrals and derivatives based on the Prabhakar function are useful to describe anomalous dielectric properties of materials whose behaviour obeys to the Havriliak–Negami model. In this work some formulas for defining these operators are described and investigated. A numerical method of product-integration type for solving differential equations with the Prabhakar derivative is derived and its convergence properties are studied. Some numerical experiments are presented to validate the theoretical results.
Fractional prabhakar derivative and applications in anomalous dielectrics: A numerical approach / Garrappa, Roberto; Maione, Guido (LECTURE NOTES IN ELECTRICAL ENGINEERING). - In: Theory and Applications of Non-integer Order Systems: 8th Conference on Non-integer Order Calculus and Its Applications, Zakopane, Poland / [a cura di] Artur Babiarz, Adam Czornik, Jerzy Klamka, Michał Niezabitowski. - Cham, Switzerland : Springer, 2017. - ISBN 978-3-319-45473-3. - pp. 429-439 [10.1007/978-3-319-45474-0_38]
Fractional prabhakar derivative and applications in anomalous dielectrics: A numerical approach
MAIONE, Guido
2017-01-01
Abstract
Fractional integrals and derivatives based on the Prabhakar function are useful to describe anomalous dielectric properties of materials whose behaviour obeys to the Havriliak–Negami model. In this work some formulas for defining these operators are described and investigated. A numerical method of product-integration type for solving differential equations with the Prabhakar derivative is derived and its convergence properties are studied. Some numerical experiments are presented to validate the theoretical results.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
