Loading [MathJax]/jax/output/SVG/config.js
Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 315, Pages 74–94
DOI: https://doi.org/10.4213/tm4227 (Mi tm4227) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Differential Games in Fractional-Order Systems: Inequalities for Directional Derivatives of the Value Functional

M. I. Gomoyunovab, N. Yu. Lukoyanovab

a N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (283 kB) Citations (7)
References:
PDF
HTML
DOI: https://doi.org/10.4213/tm4227
Abstract: For a dynamical system described by differential equations with Caputo fractional derivatives of order $\alpha \in (0,1)$, we consider a minimax–maximin differential game with a performance index that estimates the motion of the system on a fixed finite time interval. We obtain differential inequalities that characterize the value functional of the game in terms of appropriate directional derivatives.
Funding agency Grant number
Russian Science Foundation 19-11-00105
This work is supported by the Russian Science Foundation under grant 19-11-00105.
Received: February 1, 2021
Revised: April 8, 2021
Accepted: July 7, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 315, Pages 65–84
DOI: https://doi.org/10.1134/S0081543821050060
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: M. I. Gomoyunov, N. Yu. Lukoyanov, “Differential Games in Fractional-Order Systems: Inequalities for Directional Derivatives of the Value Functional”, Optimal Control and Differential Games, Collected papers, Trudy Mat. Inst. Steklova, 315, Steklov Math. Inst., Moscow, 2021, 74–94; Proc. Steklov Inst. Math., 315 (2021), 65–84
Citation in format AMSBIB
\Bibitem{GomLuk21}
\by M.~I.~Gomoyunov, N.~Yu.~Lukoyanov
\paper Differential Games in Fractional-Order Systems: Inequalities for Directional Derivatives of the Value Functional
\inbook Optimal Control and Differential Games
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 315
\pages 74--94
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4227}
\crossref{https://doi.org/10.4213/tm4227}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 315
\pages 65--84
\crossref{https://doi.org/10.1134/S0081543821050060}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000745120000006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85115420322}
Linking options:
  • https://www.mathnet.ru/eng/tm4227
  • https://doi.org/10.4213/tm4227
  • https://www.mathnet.ru/eng/tm/v315/p74
    • This publication is cited in the following 7 articles:
    1. M. I. Gomoyunov, N. Yu. Lukoyanov, “Minimax solutions of Hamilton–Jacobi equations in dynamic optimization problems for hereditary systems”, Russian Math. Surveys, 79:2 (2024), 229–324  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. M.I. Gomoyunov, “On viscosity solutions of path-dependent Hamilton–Jacobi–Bellman–Isaacs equations for fractional-order systems”, Journal of Differential Equations, 399 (2024), 335  crossref  mathscinet
    3. A. V. Kim, “Vvedenie v teoriyu pozitsionnykh differentsialnykh igr sistem s posledeistviem (na osnove metodologii $i$-gladkogo analiza”, Vestnik rossiiskikh universitetov. Matematika, 29:147 (2024), 268–295  mathnet  crossref
    4. M. I. Gomoyunov, “On optimal positional strategies in fractional optimal control problems”, Mathematical Optimization Theory and Operations Research, Lecture Notes in Computer Science, 13930, 2023, 255  crossref  mathscinet  zmath
    5. M. Gomoyunov, “Sensitivity analysis of value functional of fractional optimal control problem with application to feedback construction of near optimal controls”, Appl. Math. Optim., 88:2 (2023), 41  crossref  mathscinet  zmath
    6. M. I. Gomoyunov, “On the relationship between the Pontryagin maximum principle and the Hamilton–Jacobi–Bellman equation in optimal control problems for fractional-order systems”, Diff Equat, 59:11 (2023), 1520  crossref  crossref  mathscinet  mathscinet  zmath
    7. M. I. Gomoyunov, “On differentiability of solutions of fractional differential equations with respect to initial data”, Fract. Calc. Appl. Anal., 25:4 (2022), 1484  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Statistics & downloads:
    Abstract page:404
    Full-text PDF :128
    References:60
    First page:13
     
      Contact us:
    math-net2025_05@mi-ras.ru     		 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025