Open AccessMathematical Modeling and Functional Order Pursuits with Separated Dynamics
Author(s) -
М. Ш. Маматов,
Xakimjon Alimov
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 - 10.1088/1742-6596/2068/1/012002
Subject(s) - controllability , mathematics , dynamical systems theory , stability (learning theory) , type (biology) , order (exchange) , dynamics (music) , differential equation , ordinary differential equation , motion (physics) , fractional calculus , partial differential equation , mathematical analysis , computer science , ecology , physics , finance , quantum mechanics , machine learning , acoustics , economics , biology , artificial intelligence
This work is devoted to the study of the pursuit problem in controlled systems described by a fractional-order equation with divided dynamics. For fixed player controls, representations of solutions are established in the form of analogs of the Cauchy formula using generalized matrix functions. Sufficient conditions are obtained for the possibility of completing the pursuit. Specific types of fractional differential equations and models of fractional dynamical systems are considered. The qualitative dynamics, issues of stability and controllability of such systems are discussed. Considered, try which, the motion of the equation is described with irrational orders. Problems of the type under study are encountered in modeling the processes of economic growth and in problems of stabilizing dynamic systems.