243 citations · 1.3k across the 48 of their papers we have counts for
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A note on Hadamard fractional differential equations with varying coefficients and their applications in probability
Roberto Garra, Enzo Orsingher, Federico Polito
In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with vary…
The fractional Dodson diffusion equation: a new approach
Roberto Garra, Andrea Giusti, Francesco Mainardi
In this paper, after a brief review of the general theory concerning regularized derivatives and integrals of a function with respect to another function, we provide a peculiar fra…
The Prabhakar or three parameter Mittag--Leffler function: theory and application
Roberto Garra, Roberto Garrappa
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 pr…
Fractional Herglotz Variational Principles with Generalized Caputo Derivatives
Roberto Garra, Giorgio S. Taverna, Delfim F. M. Torres
We obtain Euler-Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional…
A generalization of the Lomnitz logarithmic creep law via Hadamard fractional calculus
Roberto Garra, Francesco Mainardi, Giorgio Spada
We present a new approach based on linear integro-differential operators with logarithmic kernel related to the Hadamard fractional calculus in order to generalize, by a parameter…