On existence and uniqueness of positive solutions to a class of fractional boundary value problems

[EN] The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ′ ( 0 ) = 0 , where 2 < α ≤ 3 and D 0 + α is the Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in the paper [Zhao et al., Abs. Appl. Anal., to appear], but in Zhao et al. (to appear), the question of uniqueness of the solution is not treated. We also present some examples where we compare our results with the ones obtained in Zhao et al. (to appear). 2010 Mathematics Subject Classification: 34B15

Effect of organic exudates of Phaeodactylum tricornutum on the Fe(II) oxidation rate constant

[EN] Fe(II) oxidation kinetics were studied in seawater and in seawater enriched with exudates excreted by Phaeodactylum tricornutum as an organic ligand model. The exudates produced after 2, 4, and 8 days of culture at 6.21 .. 107, 2.29 .. 108, and 4.98 .. 108 cell L?1 were selected. The effects of pH (7.2?8.2), temperature (5?35 ºC), and salinity (10?36.72) on the Fe(II) oxidation rate were studied. All the data were compared with the results for seawater without exudates (control). The Fe(II) rate constant decreased as a function of culture time and cell concentration in the culture at different pH, temperature, and salinity. All the experimental data obtained in this study were fitted to a polynomial function in order to quantify the fractional contribution of the organic exudates from the diatoms to the Fe(II) oxidation rate in natural seawater. Experimental results showed that the organic exudates excreted by P. tricornutum affect Fe(II) oxidation, increasing the lifetime of Fe(II) in seawater. A kinetic model approach was carried out to account for the speciation of each Fe(II) type together with its contribution to the overall rate.