The purpose of this paper is to establish unique solvability for a certain generalized boundary‐value problem for a loaded third‐order integro‐differential equation with variable coefficients. Moreover, the method of integral equations is applied to obtain an equation related to the Riemann‐Liouville operators.

Each student has their own characteristics and way of doing 3D geometric thinking. The way of thinking that students do influences the resulting understanding of the concept of 3D geometry. Therefore, this study aims to investigate students' geometric thinking based on the level of achievement of students in completing the 3D geometric thinking ability test (3D GTA). This study uses an exploratory case study design. The participants who voluntarily participated were 33 junior high school students (14 boys, 19 girls) in one of the schools in Indramayu Regency, Indonesia. Data obtained from the process of observation, tests, interviews, and documentation were analyzed qualitatively using Atlas. ti 8 software. The findings revealed that students with low 3D GTA achievements experienced difficulties in representing and calculating the surface area and volume of 3D shapes. In addition, students with moderate 3D GTA achievements experienced difficulties in representing 3D shapes but were able to translate 2D shapes from 3D shapes. Furthermore, students with high 3D GTA achievements experienced difficulties in calculating the surface area and volume of 3D shapes, but were able to use appropriate formulas and were able to interpret the comparisons of 3D geometric shapes well. The results of this study have implications for helping teachers identify student characteristics in understanding the concept of 3D geometry and connections with 2D geometry.