Center for Research and Development in Mathematics and Applications

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Publications

First and second fundamental solutions of the time-fractional telegraph equation with Laplace or Dirac operators

Publication . Ferreira, Milton; Rodrigues, Manuela M.; Vieira, Nelson

In this work we obtain the first and second fundamental solutions (FS) of the multidimensional time-fractional equation with Laplace or Dirac operators, where the two time-fractional derivatives of orders α ∈]0, 1] and β ∈]1, 2] are in the Caputo sense. We obtain representations of the FS in terms of Hankel transform, double Mellin- Barnes integrals, and H-functions of two variables. As an application, the FS are used to solve Cauchy problems of Laplace and Dirac type.

2018-05Journal article

Open access

Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials

Publication . Branquinho, A.; Moreno, A. Foulquié; Mendes, A.

In this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a com plex matrix measure. In order to study the solution of this dynamical system, we give explicit expressions for the Weyl function, general ized Markov function, and we also obtain, under some conditions, a representation of the vector of linear functionals associated with this system. We show that the orthogonality is embedded in these structure and governs the high-order Toda lattice. We also present a Lax-type theorem for the point spectrum of the Jacobi operator associated with a Toda-type lattice.

2016-11-11Journal article

Restricted access