243 citations · 1.3k across the 48 of their papers we have counts for
50 papers
On the role of Giovanni Giorgi in the history of operational methods to mathematical-physics problems
R. Garra, F. Mainardi
In this paper we discuss the historical role played by Prof. Giovanni Giorgi (1871-1950) in the development of operational methods in mathematical physics. In the literature, the a…
Stochastic solutions to abstract telegraph-type equations involving fractional dynamics
Alessandro De Gregorio, Roberto Garra
This paper investigates abstract integro-differential hyperbolic equations, focusing on the probabilistic representation of their solutions. Our analysis is based on fractional der…
Generalized time-fractional kinetic-type equations with multiple parameters
Luca Angelani, Alessandro De Gregorio, Roberto Garra
In this paper we study a new generalization of the kinetic equation emerging in run-and-tumble models. We show that this generalization leads to a wide class of generalized fractio…
Anomalous random flights and time-fractional run-and-tumble equations
Luca Angelani, Alessandro De Gregorio, Roberto Garra +1
Random flights (also called run-and-tumble walks or transport processes) represent finite velocity random motions changing direction at any Poissonian time. These models in d-dimen…
On variable-order fractional linear viscoelasticity
A. Giusti, I. Colombaro, R. Garra +2
We discuss a generalisation of fractional linear viscoelasticity based on Scarpi's approach to variable-order fractional calculus. After reviewing the general mathematical framewor…
A note on nonlinear diffusive equations on Poincaré half plane
Roberto Garra, Francesco Maltese
In this paper we show some explicit results regarding non-linear diffusive equations on Poincaré half plane. We obtain exact solutions by using the generalized separation of variab…
Exact solutions for the fractional nonlinear Boussinesq equation
A. Ceretani, F. Falcini, R. Garra
We investigate the existence of exact solutions in closed form to a fractional version of the nonlinear Boussinesq equation for groundwater flow through an unconfined aquifer. We s…
G-fractional diffusion on bounded domains in
L. Angelani, R. Garra
In this paper we study -fractional diffusion on bounded domains in with absorbing boundary conditions. We show the explicit representation of the solution and the…
A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling
Lorenzo Cristofaro, Roberto Garra, Enrico Scalas +1
In statistical seismology, the Epidemic Type Aftershocks Sequence (ETAS) model is a branching process used world-wide to forecast earthquake intensity rates and reproduce many stat…
On G-fractional diffusion models in bounded domains
L. Angelani, R. Garra
In the recent literature, the g-subdiffusion equation involving Caputo fractional derivatives with respect to another function has been studied in relation to anomalous diffusions…
The tempered space-fractional Cattaneo equation
Luisa Beghin, Roberto Garra, Francesco Mainardi +1
We consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. We find the characteristic function of the related process and we expla…
A note on a modified fractional Maxwell model
Roberto Garra, Armando Consiglio, Francesco Mainardi
In this paper we consider a modified fractional Maxwell model based on the application of Hadamard-type fractional derivatives. The model is physically motivated by the fact that w…
On the application of Mittag-Leffler functions to hyperbolic-type decay of luminescence
Ambra Lattanzi, Giampietro Casasanta, Roberto Garra
In 1861, Becquerel analyzed the time-resolved luminescence and formulated an empirical hyperbolic-type decay function, which was later named Becquerel decay law. Since then, studie…
A note on generalized fractional diffusion equations on Poincarè half plane
R. Garra, F. Maltese, E. Orsingher
In this paper we study generalized time-fractional diffusion equations on the Poincarè half plane . The time-fractional operators here considered are fractional der…
Some applications of Wright functions in fractional differential equations
R. Garra, F. Mainardi
In this note we prove some new results about the application of Wright functions of the first kind to solve fractional differential equations with variable coefficients. Then, we c…
Long time localization of modified surface quasi-geostrophic equations
Guido Cavallaro, Roberto Garra, Carlo Marchioro
We discuss the time evolution of a two-dimensional active scalar flow, which extends some properties valid for a two-dimensional incompressible nonviscous fluid. In particular we s…
Alternative probabilistic representations of Barenblatt-type solutions
Alessandro De Gregorio, Roberto Garra
A general class of probability density functions \[u(x,t)=Ct^{-αd}\left (1-\left (\frac{\|x\|}{ct^α}\right )^β\right )_+^γ,\quad x\in \mathbb{R}^d,t>0,\] is considered, containing…
A practical guide to Prabhakar fractional calculus
Andrea Giusti, Ivano Colombaro, Roberto Garra +4
The Mittag-Leffler function is universally acclaimed as the Queen function of fractional calculus. The aim of this work is to survey the key results and applications emerging from…
Probability distributions for the run-and-tumble models with variable speed and tumbling rate
Luca Angelani, Roberto Garra
In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity…
Cyclic random motions with orthogonal directions
E. Orsingher, R. Garra, A. I. Zeifman
A cyclic random motion at finite velocity with orthogonal directions is considered in the plane and in . We obtain in both cases the explicit conditional distribution…
Fractional Brownian motions ruled by nonlinear equations
Roberto Garra, Elena Issoglio, Giorgio S. Taverna
In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional diff…
Modeling biological systems with an improved fractional Gompertz law
Luigi Frunzo, Roberto Garra, Andrea Giusti +1
The aim of this paper is to provide a fractional generalization of the Gompertz law via a Caputo-like definition of fractional derivative of a function with respect to another func…
Scott-Blair models with time-varying viscosity
Ivano Colombaro, Roberto Garra, Andrea Giusti +1
In a recent paper, Zhou et al. [Mech Time-Depend Mater (2017) 21: 151] studied the time-dependent properties of Glass Fiber Reinforced Polymers composites by employing a new rheolo…
On Scott-Blair model with time-varying viscosity in linear viscoelasticity
Roberto Garra, Francesco Mainardi
In a recent paper, Zhou et al. studied the time-dependent properties of Glass Fiber Reinforced Polymers (GFRP) composites by using a new rheological model with a time-variable visc…