In this paper, the concept of the trigonometric representation of parameterized interval analysis is introduced to investigate a theory of the interval-valued Abel integral equation (IAIE) on a time scale. We provide suitable conditions to show that the IAIE on a time scale is solvable. Some simple examples are given to illustrate our main result.

Mapping to forecast the air pollution concentration in Da Nang city is an urgent issue for management agencies and researchers of environmental pollution. Although the simulation of spatial location has become popular, it uses the classical interpolation methods with low reliability. Based on the distribution of air quality monitoring stations located in industrial parks, residential areas, transport axes... and sources of air pollution, the application of geostatistical theories, this study presents the results of the Cokriging's interpolation selection which provides forecast results of air pollution distribution in Da Nang city with high reliability. In this article, we use the recorded TSP concentrations (one of major air pollution causes at large metropolis) at several observational stations in Da Nang city, employ the Cokriging interpolation method to find suitable models, then predict TSP dust concentrations at some unmeasured stations in the city. Our key contribution is finding good statistical models by several criteria, then fitting those models with high precision.