The Prabhakar function (namely, a three parameter Mittag–Leffler function) is investigated. This function plays a fundamental role in the description of the anomalous dielectric properties in disordered materials and heterogeneous systems manifesting simultaneous nonlocality and nonlinearity and, more generally, in models of Havriliak–Negami type. After reviewing some of the main properties of the function, the asymptotic expansion for large arguments is investigated in the whole complex plane and, with major emphasis, along the negative semi-axis. Fractional integral and derivative operators of Prabhakar type are hence considered and some nonlinear heat conduction equations with memory involving Prabhakar derivatives are studied.
The Prabhakar or three parameter Mittag–Leffler function: Theory and application / Garra, R.; Garrappa, R.. - In: COMMUNICATIONS IN NONLINEAR SCIENCE & NUMERICAL SIMULATION. - ISSN 1007-5704. - 56:(2018), pp. 314-329. [10.1016/j.cnsns.2017.08.018]
The Prabhakar or three parameter Mittag–Leffler function: Theory and application
Garra R.;
2018
Abstract
The Prabhakar function (namely, a three parameter Mittag–Leffler function) is investigated. This function plays a fundamental role in the description of the anomalous dielectric properties in disordered materials and heterogeneous systems manifesting simultaneous nonlocality and nonlinearity and, more generally, in models of Havriliak–Negami type. After reviewing some of the main properties of the function, the asymptotic expansion for large arguments is investigated in the whole complex plane and, with major emphasis, along the negative semi-axis. Fractional integral and derivative operators of Prabhakar type are hence considered and some nonlinear heat conduction equations with memory involving Prabhakar derivatives are studied.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.