Distributed order equations as boundary value problems

This is a PDF version of a preprint submitted to Elsevier. The definitive version was published in Computers and mathematics with applications and is available at www.elsevier.comThis preprint discusses the existence and uniqueness of solutions and proposes a numerical method for their approximation in the case where the initial conditions are not known and, instead, some Caputo-type conditions are given away from the origin

Fractional boundary value problems: Analysis and numerical methods

This is the author's PDF of an article published in Fractional calculus and applied analysis 2011. The original publication is available at www.springerlink.comThis journal article discusses nonlinear boundary value problems.Fundacao para a Ciencia e Tecnologi

A nonpolynomial collocation method for fractional terminal value problems

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Computational and Applied Mathematics, 275, February 2015, doi: 10.1016/j.cam.2014.06.013In this paper we propose a non-polynomial collocation method for solving a class of terminal (or boundary) value problems for differential equations of fractional order α, 0 < α < 1. The approach used is based on the equivalence between a problem of this type and a Fredholm integral equation of a particular form. Taking into account the asymptotic behaviour of the solution of this problem, we propose a non-polynomial collocation method on a uniform mesh. We study the order of convergence of the proposed algorithm and a result on optimal order of convergence is obtained. In order to illustrate the theoretical results and the performance of the method we present several numerical examples.The work was supported by an International Research Excellence Award funded through the Santander Universities scheme

An implicit finite difference approximation for the solution of the diffusion equation with distributed order in time

In this paper we are concerned with the numerical solution of a diffusion equation in which the time order derivative is distributed over the interval [0,1]. An implicit numerical method is presented and its unconditional stability and convergence are proved. A numerical example is provided to illustrate the obtained theoretical results

Fractional pennes' bioheat equation: Theoretical and numerical studies

Accepted for publication in Fractional calculus and applied analysisOriginally published in the journal Fract. Cal. Appl. Anal. Vol. 18 No. 4 / 2015 / pp.1080–1106 / DOI 10.1515/fca-2015-0062. The original publication is available at: http://www.degruyter.com/view/j/fca.2015.18.issue-4/fca-2015-0062/fca-2015-0062.xml?rskey=sWWcn0&result=1In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bio heat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.The authors L.L. Ferras and J. M. Nobrega acknowledge financial funding by FEDER through the COMPETE 2020 Programme and by FCT- Portuguese Foundation for Science and Technology under the projects UID/CTM/50025/2013 and EXPL/CTM-POL/1299/2013. L.L. Ferras acknowledges financial funding by the Portuguese Foundation for Science and Technology through the scholarship SFRH/BPD/100353/2014. M. Rebelo acknowledges financial funding by the Portuguese Foundation for Science and Technology through the project UID/MAT/00297/2013

Análise das funcionalidades de gamificação nos ambientes de aprendizagem Classcraft e Moodle à luz da framework Octalysis

O 4.º Encontro sobre Jogos e Mobile Learning, EJML 2018, no dia 5 de maio de 2018, sábado, volta a reunir em Coimbra investigadores, mestrandos e doutorandos, professores, psicólogos, profissionais de Ciências da Educação e demais interessados nestas temáticas. Este evento internacional, realizado pela Universidade de Coimbra e pela Universidade de Sevilha, atrai participantes nacionais e estrangeiros que pretendem partilhar conhecimentos, investigação, práticas e debater questões importantes para uma integração sustentável de jogos educativos e dispositivos móveis na educação.A gamificação é uma técnica recente que consiste em aplicar elementos de jogos em contextos não relacionados com jogos. Existem frameworks teóricas que sugerem um modelo de aplicação desses elementos na implementação de soluções concretas. Neste artigo analisámos dois Sistemas de Gestão da Aprendizagem, Classcraft e Moodle, sob a lente da framework Octalysis. Apesar das duas plataformas disponibilizarem vários elementos de jogo, que combinados entre si procuram incrementar a motivação do aluno, a plataforma Classcraft é a que apresenta mais elementos de jogos, abrangendo todos os eixos desta framework.info:eu-repo/semantics/publishedVersio

Improving In-Plant Logistics Flow by Physical and Digital Pathways

The automotive industry is constantly using continuous improvement to leverage its growth and sustainability. The improvement of the intralogistics of component companies for the automotive industry is based on the same principles. The Milk-Run System (MRS) allows the inbound transportation of the raw materials containers to the production lines, as well as the return of finished product containers. Thus, it is important to improve the performance of existing vehicle routing system, according to customer demand orders and the assignment of the production line. The present study identified and examined the existing constraints and proposes the improvements to increase the performance of the existing inbound milk-run system. The system capacity and the routing have been redefined as well as the information need to an efficient management system. Since the production is not standardized, the software was developed to assist the management of the milk-run system. Its implementation showed that with one vehicle and four wagons all the production lines are properly assisted. The contributions of this study were the reduction in 15% of the milk-run lap time, the decrease of the number of milk-run laps, allowing the increase of the number of lines assisted by this intralogistics system, permitting the assignment of new tasks to the MRS operator during the idle time. Moreover, unnecessary laps, unwanted stops and exchange of packaging were eliminated.info:eu-repo/semantics/publishedVersio

Semi-analytical solutions for the poiseuille-couette flow of a generalised Phan-Thien-Tanner fluid

This work presents new analytical and semi-analytical solutions for the pure Couette and Poiseuille-Couette flows, described by the recently proposed (Ferras et al., A Generalised Phan-Thien-Tanner Model, JNNFM 2019) viscoelastic model, known as the generalised Phan-Thien-Tanner constitutive equation. This generalised version considers the Mittag-Leffler function instead of the classical linear or exponential functions of the trace of the stress tensor, and provides one or two new fitting constants in order to achieve additional fitting flexibility. The analytical solutions derived in this work allow a better understanding of the model, and therefore contribute to improve the modelling of complex materials, and will provide an interesting challenge to computational rheologists, to benchmarking and to code verification.This research was funded by FEDER through COMPETE2020-Programa Operacional Competitividade e Internacionalizacao (POCI) and by national funds through FCT-Fundacao para a Ciencia e a Tecnologia, I. P. through Projects PTDC/EMS-ENE/3362/2014, POCI-01-0145-FEDER-016665, UID-MAT-00013/2013, and UID/MAT/00297/2013 as well as grant number SFRH/BPD/100353/2014. This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the project UID/MAT/00297/2019 (Centro de Matematica e Aplicacoes)

Recent Advances in Complex Fluids Modeling

In this chapter, we present a brief description of existing viscoelastic models, starting with the classical differential and integral models, and then focusing our attention on new models that take advantage of the enhanced properties of the Mittag-Leffler function (a generalization of the exponential function). The generalized models considered in this work are the fractional Kaye-Bernstein, Kearsley, Zapas (K-BKZ) integral model and the differential generalized exponential Phan-Thien and Tanner (PTT) model recently proposed by our research group. The integral model makes use of the relaxation function obtained from a step-strain applied to the fractional Maxwell model, and the differential model generalizes the familiar exponential Phan-Thien and Tanner constitutive equation by substituting the exponential function of the trace of the stress tensor by the Mittag-Leffler function. Since the differential model is based on local operators, it reduces the computational time needed to predict the flow behavior, and, it also allows a simpler description of complex fluids. Therefore, we explore the rheometric properties of this model and its ability (or limitations) in describing complex flows

Inter-relações entre trematódeos e os seus hospedeiros através de um SIG, em Timor Leste (Timor Lorosae)

Integrado em estudos interdisciplinares aplicados a zonas tropicais foi implementado um Sistema de Informação Geográfica (SIG) em ambiente GeoMedia com base na informação disponível sobre trematodoses (1965-1977), particularmente as provocadas por Fasciola gigantica e Eurytrema pancreaticum, referentes a Timor Leste (Timor Lorosae). Neste sentido procedeu-se à compilação de dados, à sua estruturação consoante os diversos tipos de estudo efectuado, e à construção de mapas temáticos. O SIG inclui para além da informação geográfica relevante, dados georeferenciáveis que fazem parte da informação disponível até 1977. Este estudo permite a utilização desta base de dados no planeamento de trabalhos futuros sobre esta temática a desenvolver naquela área geográfica assim como a sua actualização com novos dados a serem obtidos em Timor Lorosae