21 documents found, page 1 of 3
Quaternionic convolutional neural networks with trainable Bessel activation fun...
Vieira, NelsonQuaternionic Convolutional Neural Networks (QCNN) possess the ability to capture both external dependencies between neighboring features and internal latent dependencies within features of an input vector. In this study, we employ QCNN with activation functions based on Bessel-type functions with trainable parameters, for performing classification tasks. Our experimental results demonstrate that this activation...
Some representations for the eigenfunctions of the time-fractional wave operator
Rodrigues, M.M.; Ferreira, M.; Vieira, NelsonIn this work we present some new representations for the eigenfunctions of the time-fractional wave operator with the time-fractional derivative in the Caputo sense.
On a regular Ψ-fractional Sturm-Liouville problem
Ferreira, M.; Rodrigues, M. Manuela; Vieira, NelsonIn 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.
Time-fractional telegraph equation with ψ-Hilfer derivatives
Vieira, Nelson; Ferreira, Milton; Rodrigues, M. ManuelaThis paper deals with the investigation of the solution of the time-fractional telegraph equation in higher dimensions with $\psi$-Hilfer fractional derivatives. By application of the Fourier and $\psi$-Laplace transforms the solution is derived in closed form in terms of bivariate Mittag-Leffler functions in the Fourier domain and in terms of convolution integrals involving Fox H-functions of two-variables in ...
Time-fractional telegraph equation of distributed order in higher dimensions wi...
Vieira, Nelson; Rodrigues, M. Manuela; Ferreira, MiltonIn this paper, we consider time-fractional telegraph equations of distributed order in higher spatial dimensions, where the time derivatives are in the sense of Hilfer, thus interpolating between the Riemann-Liouville and the Caputo fractional derivatives. By employing the techniques of the Fourier, Laplace, and Mellin transforms, we obtain a representation of the solution of the Cauchy problem associated with ...
Time-fractional diffusion equation with psi-Hilfer derivative
Vieira, Nelson; Rodrigues, M. Manuela; Ferreira, MiltonIn this work, we consider the multidimensional time-fractional diffusion equation with the $\psi$-Hilfer derivative. This fractional derivative enables the interpolation between Riemann-Liouville and Caputo fractional derivatives and its kernel depends on an arbitrary positive monotone increasing function $\psi$ thus encompassing several fractional derivatives in the literature. This allows us to obtain general...
Time-fractional diffusion equation with ψ-Hilfer derivative
Vieira, Nelson; Rodrigues, M. Manuela; Ferreira, MiltonIn this work, we consider the multidimensional time-fractional diffusion equation with the $\psi$-Hilfer derivative. This fractional derivative enables the interpolation between Riemann-Liouville and Caputo fractional derivatives and its kernel depends on an arbitrary positive monotone increasing function $\psi$ thus encompassing several fractional derivatives in the literature. This allows us to obtain general...
A Fractional Analysis in Higher Dimensions for the Sturm-Liouville Problem
Ferreira, Milton; Rodrigues, M. Manuela; Vieira, NelsonIn this work, we consider the n-dimensional fractional Sturm-Liouville eigenvalue problem, by using fractional versions of the gradient operator involving left and right Riemann-Liouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem. More precisely, we show that the eigenfunctions are orthogonal and the eigenvalues a...
Time-fractional telegraph equation of distributed order in higher dimensions
Vieira, Nelson; Rodrigues, M. Manuela; Ferreira, MiltonIn this work, the Cauchy problem for the time-fractional telegraph equation of distributed order in Rn is considered. By employing the technique of the Fourier, Laplace, and Mellin transforms, a representation of the fundamental solution of this equation in terms of convolutions involving the Fox H-function is obtained. Some particular choices of the density functions in the form of elementary functions are stu...
Application of the Fractional Sturm–Liouville Theory to a Fractional Sturm–Liou...
Ferreira, M.; Rodrigues, M. Manuela; Vieira, NelsonIn this paper, we consider a non-homogeneous time-space-fractional telegraph equation in n-dimensions, which is obtained from the standard telegraph equation by replacing the first- and second-order time derivatives by Caputo fractional derivatives of corresponding fractional orders, and the Laplacian operator by a fractional Sturm-Liouville operator defined in terms of right and left fractional Riemann-Liouvil...