Open AccessSolution of Dynamic Games of Fractional Order by the Method of Grids
Author(s) -
М. Ш. Маматов
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1995/1/012058
Subject(s) - discretization , fractional calculus , mathematics , convergence (economics) , partial differential equation , domain (mathematical analysis) , order (exchange) , partial derivative , grid , mathematical optimization , mathematical analysis , geometry , finance , economics , economic growth
In this article, we have studied the game problem of the equation of motion, which is described with partial derivatives of fractional order in a multidimensional domain. The time derivative is defined as the partial Riemann - Liouville fractional derivatives. To solve this problem, the grid method is applied for an equation with fractional derivatives. The convergence of the scheme is established and the error estimates are obtained in terms of the sampling step. Sufficient conditions are found close to each other for the completion of the pursuit. A method of controlling the pursuing player is constructed according to the feedback principle, which guarantees the desired result even in the situation of the most unfavorable controls of the fleeing player. In each of the above cases, a numerical method is constructed to find the price of the game in suitable classes of strategies and to construct the corresponding control laws. The discretization schemes for a differential game described by equations of fractional order in a multidimensional domain are constructed and studied.