O significado da filosofia da humanitude, no contexto dos cuidados de enfermagem à pessoa dependente e vulnerável

Revisão sistemática seguindo a metodologia dos sete passos do Cochrane Handbook, formulando a seguinte questão: Qual o significado do conceito integrador de humanitude, no contexto dos complexos e delicados cuidados que os enfermeiros prestam, a pessoas doentes vulneráveis e dependentes? No processo de resposta à questão, seguindo a metodologia sistemática, com base numa estratégia de pesquisa refinada e exaustiva a bases de dados relevantes, não se obtiveram respostas aos descritores relacionados com cuidados de enfermagem, que intersectem o conceito humanitude. No entanto, através de motores de busca e contacto com investigadores nacionais e estrangeiros, foi possível recolher um pequeno acervo de documentos, que revelam a pertinência da questão de investigação e indicam a existência de trabalho avançado na aplicação da filosofia da humanitude aos cuidados de enfermagem. O trabalho mais relevante é o método de Gineste e Marescotti, no cuidado a doentes dependentes e vulneráveis, desde 1975. Com este estudo de revisão, observa-se uma nova oportunidade de investigação, através da implementação e monitorização do método, com uma população de pessoas doentes dependentes, em Portugal

A Time-Fractional Borel–Pompeiu Formula and a Related Hypercomplex Operator Calculus

The final version is published in Complex Analysis and Operator Theory, 13-No.6, (2019). Received: 8 May 2018 / Accepted: 24 December 2018 / Published online: 11 January 2019.In this paper, we develop a time-fractional operator calculus in fractional Clifford analysis. Initially, we study the $L_p$-integrability of the fundamental solutions of the multi-dimensional time-fractional diffusion operator and the associated time-fractional parabolic Dirac operator. Then we introduce the time-fractional analogs of the Teodorescu and Cauchy-Bitsadze operators in a cylindrical domain, and we investigate their main mapping properties. As a main result, we prove a time-fractional version of the Borel-Pompeiu formula based on a time-fractional Stokes' formula. This tool in hand allows us to present a Hodge-type decomposition for the forward time-fractional parabolic Dirac operator with left Caputo fractional derivative in the time coordinate. The obtained results exhibit an interesting duality relation between forward and backward parabolic Dirac operators and Caputo and Riemann-Liouville time-fractional derivatives. We round off this paper by giving a direct application of the obtained results for solving time-fractional boundary value problems.UID/MAT/04106/2019. A-15/17 / DAAD-PPP IF/00271/2014info:eu-repo/semantics/publishedVersio

Fractional gradient methods via ψ-Hilfer derivative

Motivated by the increasing of practical applications in fractional calculus, we study the classical gradient method under the perspective of the $\psi$-Hilfer derivative. This allows us to cover in our study several definitions of fractional derivatives that are found in the literature. The convergence of the $\psi$-Hilfer continuous fractional gradient method is studied both for strongly and non-strongly convex cases. Using a series representation of the target function, we develop an algorithm for the $\psi$-Hilfer fractional order gradient method. The numerical method obtained by truncating higher-order terms was tested and analyzed using benchmark functions. Considering variable order differentiation and optimizing the step size, the $\psi$-Hilfer fractional gradient method shows better results in terms of speed and accuracy. Our results generalize previous works in the literature.publishe

A fractional analysis in higher dimensions for the Sturm-Liouville problem

In 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 are real and simple. Moreover, using techniques from fractional variational calculus, we prove in the main result that the eigenvalues are separated and form an infinite sequence, where the eigenvalues can be ordered according to increasing magnitude. Finally, a connection with Clifford analysis is established.publishe

Distributed-order relaxation-oscillation equation

Acknowledgments The work of the authors was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Fundação para a Ciência e a Tecnologia, within projects UIDB/04106/2020 and UIDP/04106/2020. N. Vieira was also supported by FCT via the 2018 FCT program of Stimulus of Scientific Employment - Individual Support (Ref: CEECIND/01131/2018).In this short paper, we study the Cauchy problem associated with the forced time-fractional relaxation-oscillation equation with distributed order. We employ the Laplace transform technique to derive the solution. Additionally, for the scenario without external forcing, we focus on density functions characterized by a single order, demonstrating that under these conditions, the solution can be expressed using two-parameter Mittag-Leffler functions.info:eu-repo/semantics/publishedVersio

Dirac’s method applied to the time-fractional diffusion-wave equation

Acknowledgments: The work of the authors was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT–Fundação para a Ciência e a Tecnologia, within projects UIDB/04106/2020 and UIDP/04106/2020. N. Vieira was also supported by FCT via the 2018 FCT program of Stimulus of Scientific Employment - Individual Support (Ref: CEECIND/01131/2018).We compute the fundamental solution for time-fractional diffusion Dirac-like equations, which arise from the factorization of the multidimensional time-fractional diffusion-wave equation using Dirac’s factorization approach.info:eu-repo/semantics/publishedVersio