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.

Influence of electric fields over the nucleation ratio of the lithium-potassium sulfate and its pedagogical value

[EN]This paper presents our research about nucleation and its dependency with external conditions, as well as the internal characteristics of the solution itself. Among the research lines of our group, we has been studying the influence of electric fields over two different but related compounds: Lithium-Potassium Sulfate and Lithium-Amonium Sulfate, which both of them show a variation on the nucleation ratio when an electric field is applied during the crystal growth. Moreover, in this paper will be explained a laboratory protocol to teach universitary Science students the nucleation process itself and how it depends on external applied conditions, e.g. electric fields.