Existence and uniqueness of positive solutions for a class of fractional differential equation with integral boundary conditions

The purpose of this paper is to investigate the existence and uniqueness of positive solutions for a class of fractional differential equation with integral boundary conditions. Our analysis relies on two fixed point theorems of a sum operator in partial ordering Banach space. The main results obtained can not only guarantee the existence of a unique positive solution, but also be applied to construct an iterative scheme for approximating it

Formation law and criterion of nebulous macroscopic segregation in ZL205A alloy castings

The appearance of macroscopic segregation in ZL205A alloy castings bears a super resemblance to the appearance of shrinkage porosity, and the chemical composition of the segregation is Al2Cu whose microstructure is in the form of dentrite or skeleton crystal. According to the characteristic of nebulous segregation, the formation process could be divided into two steps by the eutectic temperature of Al2Cu. Then a criterion for each of the two steps is brought forward on the basis of the shrinkage porosity criterion of low pressure casting