Center for Research and Development in Mathematics and Applications

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Publications

On a fractional Sturm-Liouville problem in higher dimensions

Publication . Vieira, N.; Rodrigues, M. M.; Ferreira, M.

In this short paper, we consider an n-dimensional fractional Sturm-Liouville eigenvalue problem, by using fractional versions of the gradient operator involving left Caputo and right Riemann-Liouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem.

2023-09Journal article

Open access

Uniformly distributed-order wave equation in higher dimensions

Publication . Vieira, N.; Rodrigues, M. M.; Ferreira, M.

In this short paper, we obtain the eigenfunctions of the uniformly distributed-order wave equation in Rn ×R+, as Laplace integral of Fox H-functions. For the particular case of the first fundamental solution, the fractional moment of second order of the fundamental solution is studied using the Tauberian Theorem.

2023-09Journal article

Open access

Eigenfunctions of the time-fractional telegraph equation of distributed order

Publication . Vieira, N.; Rodrigues, M. M.; Ferreira, M.

In this work, the eigenfunction problem for the time-fractional telegraph operator of distributed order in Rn ×R+ is considered. By employing the technique of the Fourier, Laplace and Mellin transforms, an integral representation of the eigenfunctions involving the Fox H-function is obtained.

2023-09Journal article

Open access

On a regular Ψ-fractional Sturm-Liouville problem

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

In this short paper, we consider a $\psi$-fractional Sturm-Liouville eigenvalue problem by using left $\psi$-Caputo and right $\psi$-Riemann-Liouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem.

2022-06Journal article

Open access

Using an interdisciplinary approach to the teaching of solid geometry in a professional development course for preschool and primary school teachers

Publication . Hall, Andreia; Pais, Sónia

This paper presents some results of a professional development course for teachers where the participants studied basic solid geometry and developed applied projects in an interdisciplinary context. The course took place in a Portuguese university, from February to May 2020, and involved 19 teachers of preschool and primary levels (grades 1 to 4). The authors have developed a qualitative case study to evaluate how an interdisciplinary approach to the teaching of solid geometry is perceived, by the mathematics teachers, as a contribution to the teaching/learning process of geometry. Overall, the activities developed have proved to be successful examples of interdisciplinary methodologies. Moreover, the approach followed during the course helped the teachers develop their geometric competences concerning solid geometry in a more consistent appropriation and application of the geometric concepts involved.

2021Journal article

Open access