Abstract
The sets of Minkowski algebraic sum and geometric difference are considered. The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential games. This paper investigates the geometric properties of the Minkowski algebraic sum and the geometric difference of sets. Various examples are considered that calculate the geometric differences of sets. The results of the research are presented and proved as a theorem. At the end of the article, the results were applied to fractional differential games.
Highlights
Minkowski sums and geometric differences are important operations
The purpose of the research in this paper is to apply the properties of Minkowski sum and geometric difference to fractional differential games
This paper investigates the geometric properties of the Minkowski algebraic sum and the geometric difference of sets
Summary
Minkowski sums and geometric differences are important operations. They are used in many fields, such as: image processing, robotics, computer-aided design, mathematical morphology and spatial planning. Minkowski sums and geometric differences are used in various fields of science, such as differential games and optimal control [1] [2] [3], computer-aided design and production [2], computer animation and morphing [3], morphological image analysis [4] [5], measures for convex polyhedral [6], dynamic modeling [7], robot motion planning [8] and so on.
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