243 citations · 1.3k across the 48 of their papers we have counts for
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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 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…
Confinement of a hot temperature patch in the modified SQG model
Roberto Garra
In this paper we study the time evolution of a temperature patch in according to the modified Surface Quasi-Geostrophic Equation (SQG) patch equation. In particular we give a…
Fractional Klein-Gordon equation for linear dispersive phenomena: analytical methods and applications
Roberto Garra, Enzo Orsingher, Federico Polito
In this paper we discuss some exact results related to the fractional Klein--Gordon equation involving fractional powers of the D'Alembert operator. By means of a space-time transf…
On Some Operators Involving Hadamard Derivatives
Roberto Garra, Federico Polito
In this paper we introduce a novel Mittag--Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivativ…
Fractional calculus modelling for unsteady unidirectional flow of incompressible fluids with time-dependent viscosity
Roberto Garra, Federico Polito
In this note we analyze a model for a unidirectional unsteady flow of a viscous incompressible fluid with time dependent viscosity. A possible way to take into account such behavio…
Analytic solutions of fractional differential equations by operational methods
Roberto Garra, Federico Polito
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we d…
Coupled systems of fractional equations related to sound propagation: analysis and discussion
Roberto Garra, Federico Polito
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordina…