arXiv subjects

Roberto Garrappa

Publications and source records attributed to Roberto Garrappa.

21 records · Page 2Linked to original sources

arXiv2015

Numerical evaluation of two and three parameter Mittag-Leffler functions

The Mittag-Leffler (ML) function plays a fundamental role in fractional calculus but very few methods are available for its numerical evaluation. In this work we present a method for the efficient computation of the ML function based on the numerical inversion of its Laplace transform (LT): an optimal parabolic contour is selected on the basis of the distance and the strength of the singularities of the LT, with the aim of minimizing the computational effort and reduce the propagation of errors. Numerical experiments are presented to show accuracy and efficiency of the proposed approach. The application to the three parameter ML (also known as Prabhakar) function is also presented.

math.NA↗

arXiv2014

Suppressing chaos in discontinuous systems of fractional order by active control

In this paper, a chaos control algorithm for a class of piece-wise continuous chaotic systems of fractional order, in the Caputo sense, is proposed. With the aid of Filippov's convex regularization and via differential inclusions, the underlying discontinuous initial value problem is first recast in terms of a set-valued problem and hence it is continuously approximated by using Cellina's Theorem for differential inclusions. For chaos control, an active control technique is implemented so that the unstable equilibria become stable. As example, Shimizu--Morioka's system is considered. Numerical simulations are obtained by means of the Adams-Bashforth-Moulton method for differential equations of fractional-order.

nlin.CD↗

arXiv2013

Exponential quadrature rules for linear fractional differential equations

This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized Mittag-Leffler function. Then suitable quadrature rules are devised and order conditions of algebraic type are derived. Theoretical findings are validated by means of numerical experiments and the effectiveness of the proposed approach is illustrated by means of comparisons with other standard methods.

math.NA↗