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

Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems

[EN] We establish the existence and uniqueness of a positive and nondecreasing solution to a singular boundary value problem of a class of nonlinear fractional differential equation. Our analysis relies on a fixed point theorem in partially ordered sets.

Use of different commercial Artemia sp. Enrichements in Octopus Vulgaris, paralarval rearing at initial planctonic phase: effects on growth, survival and fatty acid composition of the paralarvae

[EN] Octopus "paralarvae", are planktonic, swim actively and have high metabolic rates, requiring large quantities of live prey of adequate motility and nutritional quality ( Iglesias et al., 2000; Navarro and Villanueva, 2000, 2003). During the planktonic phase, they undergo strong morphological changes, after which the octopuses start settling to the bottom. The potential of Octopus vulgaris as candiadate for diversification of marine aquacultures are mainly due to its high food conversion rate and fast growth.( Iglesias et al 2006). Despite the research effort taken until now, paralarval rearing of O. vulgaris still suffers high mortalities which limited the industrial culture of this species. The main problems in the paralarval rearing stages are the high mortality rates and poor growth. These are attributed to the lack of standardized culture techniques and nutritional deficiencies in the diet of paralarvae, especially in n-3 highly unsaturated fatty acids (n-3 HUFA). The objective if this experience was to test different commercial live prey enrichment to improve nutritional quality of the artemia.