In this paper, we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, the analytical solution for a class of fractional models associated with the logistic model, the von Foerster model and the Bertalanffy model is presented graphically for various fractional orders. The solution of the corresponding classical model is recovered as a particular case.

Dengue is a public health problem that presents complexity in its dissemination. The physical means of spreading and the dynamics of the spread between municipalities need to be analyzed to guide effective public policies to combat this problem. This study uses timing varying graph methods (TVG) to construct a correlation network between occurrences of reported cases of dengue between cities in the state of Bahia-Brazil. The topological network indices of all cities were correlated with dengue incidence using Spearman correlation. A randomization test was used to estimate the significance value of the correlation. The correlation network presented a complex behavior with a heavy-tail distribution of the network edges weight. The randomization test exhibit a significant correlation (P < 0.0001) between the degree of each municipality in the network and the incidence of dengue in each municipality. The hypothesis of the existence of a correlation between the occurrences of reported cases of dengue between different municipalities in the state of Bahia was validated. The significant correlation between the node degree and incidence, indicates that municipalities with high incidence are also responsible for the spread of the disease in the state. The method proposed suggests a new tool in epidemiological control strategy.

The hydrophobic effect is the major factor that drives a protein toward collapse and folding. As a consequence of the folding process a hydrophobic core is shielded by the solvent-accessible surface area of the protein. We analyze the solvent-accessible surface area of 1825 nonhomolog protein chains deposited in the Brookhaven Protein Data Bank. This solvent-accessible surface area presents an intrinsic self-similarity behavior. The comparison between the accessible surface area as function of the number of amino acids and the accessible surface area as function of gyration radius supplies a measure of the scaling exponent close to the one observed by volume as function of radius of gyration or by mass-size exponent. The present finding indicates that the fractal analysis describes the protein compactness as an object packing between random spheres in percolation threshold and crumpled wires.

The global energy landscape is rapidly changing, including the transition to a low carbon economy and the use of liquid biofuel. The production of liquid biofuel has emerged as an alternative to the use of fossil fuels for purposes of energy conservation, carbon emission mitigation and agricultural development. In this article we study the co-movements between hydrous ethanol and gasoline C in the Brazilian retail market. A multi-scale cross correlation analysis was applied to the Average Retail Margin time series of hydrous ethanol for fifteen relevant retail markets in Brazil to analyze the competitiveness of hydrous ethanol towards gasoline C. The empirical results showed a remarkable different behavior between hydrous ethanol and gasoline C, for any time scale, regardless of geographical distance or regional differences.