Abstract
AbstractNonstationary fractional-order systems represent a new class of dynamic systems characterized by time-varying parameters as well as memory effect and hereditary properties. Differential game described by system of linear nonstationary differential equations of fractional order is treated in the paper. The game involves two players, one of which tries to bring the system’s trajectory to a terminal set, whereas the other strives to prevent it. Using the technique of set-valued maps and their selections, sufficient conditions for reaching the terminal set in a finite time are derived. Theoretical results are supported by a model example.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Analysis
Reference39 articles.
1. Al-Refai, M., Luchko, Y.: Comparison principles for solutions to the fractional differential inequalities with the general fractional derivatives and their applications. J. Differ. Equ. 319, 312–324 (2022). https://doi.org/10.1016/j.jde.2022.02.054
2. Aubin, J.-P., Frankowska, H.: Set-Valued Analysis. Birkhäuser, Boston (1990)
3. Baake, M., Schlägel, U.: The Peano-Baker series. Proc. Steklov Inst. Math. 275(1), 155–159 (2011)
4. Bourdin, L.: Cauchy-Lipschitz theory for fractional multi-order dynamics: State-transition matrices, Duhamel formulas and duality theorems. Differ. Integral Equ. 31(7/8), 559–594 (2018)
5. Blagodatskikh, V.I., Filippov, A.F.: Differential inclusions and optimal control. Proc. Steklov Inst. Math. 169, 194–252 (1985)