Some pioneers of the applications of fractional calculus

In the last decades fractional calculus (FC) became an area of intensive research and development. This paper goes back and recalls important pioneers that started to apply FC to scientific and engineering problems during the nineteenth and twentieth centuries. Those we present are, in alphabetical order: Niels Abel, Kenneth and Robert Cole, Andrew Gemant, Andrey N. Gerasimov, Oliver Heaviside, Paul Lévy, Rashid Sh. Nigmatullin, Yuri N. Rabotnov, George Scott Blair.

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

Fractional Order Generalized Information

This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.

Rhapsody in fractional

This paper studies several topics related with the concept of “fractional” that are not directly related with Fractional Calculus, but can help the reader in pursuit new research directions. We introduce the concept of non-integer positional number systems, fractional sums, fractional powers of a square matrix, tolerant computing and FracSets, negative probabilities, fractional delay discrete-time linear systems, and fractional Fourier transform.

A Review of Definitions for Fractional Derivatives and Integral

This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.

Riesz potential versus fractional Laplacian

This paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.

Delay approximation of fractional integrals

This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag-Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.

Fractional calculus analysis of the cosmic microwave background

Cosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.

Fractional order modelling of dynamic backlash

This paper studies the dynamical properties of systems with backlash and impact phenomena. This type of non-linearity can be tackled in the perspective of the fractional calculus theory. Fractional and integer order models are compared and their influence upon the emerging dynamics is analysed. It is demonstrated that fractional models can memorize dynamical effects due to multiple micro-collisions.

Lysotypes and plasmidial profile of Salmonella Serovar Typhimurium isolated from children with enteric processes in the cities of Rio de Janeiro, RJ, and Salvador, BA - Brazil

The lysotypes, plasmidial profiles, and profiles of resistance to antimicrobial agents were determined in 111 Salmonella Typhimurium strains isolated from feces and blood of children treated in Rio de Janeiro and in Salvador. Six distinct lysotypes (19, 41, 97, 105, 120 and 193) were recognized, with a predominance of lysotype 193 (59.7%) in Rio de Janeiro and of phage type 105 (38.4) in Salvador. Approximately 86.7% of the lysotype 193 strains presented multiple resistance to more than six antimicrobial agents, whereas 93% of lysotype 105 strains were fully susceptible. More than 90% of the strains presented plasmids distributed into 36 different profiles in Rio de Janeiro and into 10 profiles in Salvador. A 40 MDa plasmid was the most frequent (47%) in the strains from Rio de Janeiro, whereas a 61 MDa plasmid predominated (14.5%) in Salvador. Combined analysis of plasmid profile and classification into lysotypes (especially those belonging to types 105 and 103, proved to be more discriminatory than the other methods applied).

Development of thermoresponsive (polysulfone/polyacrylonitrile) - based membranes for bioseparation processes

Mestrado integrado em Engenharia Química e Bioquímica

The impact of firm-promoted accreditation of prior learning processes on the worker-organization relationship

The process of Competences Recognition, Validation and Certification , also known as Accreditation of Prior Learning (APL), is an innovative means of attaining school certificates for individuals without an academic background. The main objective of this process is to validate what people have learned in informal contexts, in order to attribute academic certificates. With the increasing interest of the qualification of workers and governmental support, more and more Portuguese organizations promote this process within their facilities and their work hours. This study explores the relationship between the promotion of this Human Resource Development Programme and employee’s attitudes (Job Satisfaction and Organizational Commitment) and behaviours (Extra-role Organizational Citizenship Behaviours) towards the organization they work for. Results of a cross-sectional survey of Portuguese Industrial Workers (N=135) showed that statistical significant results are in the higher levels of Voice Behaviours (a dimension of Extra-role Organizational Citizenship Behaviour in the groups of workers who were involved or had graduated from the firm promoted APL process.

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.

Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.