We consider a linear pursuit problem in which a group of pursuers attempts to capture a single evader in a differential game described by equations with fractional Caputo derivatives of order from the interval (0, 1). The players’ controls are subject to integral constraints, and the pursuers employ quasi-strategies. The goal of the group of pursuers is to bring at least one pursuer within any predetermined distance of the evader. It is proven that if the total energy of the pursuers exceeds the energy of the evader, then capture occurs in the game.
Keywords: differential game, pursuer, evader, capture, fractional derivative
Received March 24, 2026
Revised June 8, 2026
Accepted June 15, 2026
Funding Agency: This research was funded by the Ministry of Science and Higher Education of the Russian Federation in the framework of the state assignment, project FEWS-2024-0009.
Aleksandr Sergeevich Bannikov, Cand. Sci (Phys.-Math.), Udmurt State University, Izhevsk, 426034 Russia, e-mail: asbannikov@udsu.ru
Nikolai Nikandrovich Petrov, Dr. Phys.-Math. Sci., Prof., Udmurt State University, Izhevsk, 426034 Russia, e-mail: kma3@list.ru
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Cite this article as: A.S. Bannikov, N.N. Petrov. Group pursuit in a game with fractional derivatives, a simple matrix, and integral constraints. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2026, vol. 32, no. 3, pp. 7–20.
