About the Book:This monograph addresses the theory and applications of multidimensional geometry, specifically focusing on triangulations in Euclidean spaces. The text integrates advancements in the finite element method, numerical optimization, and mesh generation with emerging fields like quantum physics and artificial intelligence.Key features include:- An innovative framework for constructing and analyzing multidimensional simplicial triangulations.- New methodologies for fractional-order boundary value problems and their computational implementations.- Applications in subatomic particle dynamics, robotics, and explainable artificial intelligence.