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 JAMP  Vol.6 No.3 , March 2018
Differential Games of Persecution of Frozen Order with Separate Dynamics
Abstract: This article is devoted to obtaining sufficient conditions for the completion of pursuit for control systems of fractional order described with divided dynamics. The results are illustrated on model examples of gaming problems with a simple matrix and separated fractional-order motions.
Cite this paper: Mamatov, M. and Alimov, K. (2018) Differential Games of Persecution of Frozen Order with Separate Dynamics. Journal of Applied Mathematics and Physics, 6, 475-487. doi: 10.4236/jamp.2018.63044.
References

[1]   Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006) Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, 500.

[2]   Agrawal, O.P. (2008) A Formulation and Numerical Scheme for Fractional Optimal Control Problems. Journal of Vibration and Control, 14, 1291-1299.
https://doi.org/10.1177/1077546307087451

[3]   Lakshmikantham, V., Leela, S. and Vasundhara, D.J. (2009) Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge, 500.

[4]   Monje, C.A., Chen, Y.Q., Vinagre, B.M., Xue, D. and Feliu, V. (2010) Fractional-Order Systems and Controls: Fundamentals and Applications. Springer-Verlag, London, 400 c.

[5]   Caponetto, R., Dongola, G., Fortuna, L. and Petras, I. (2010) Fractional Order Systems. Modeling and Control Applications. World Scientific, Singapore, 200.
https://doi.org/10.1142/7709

[6]   Frederico, G.S.F. and Torres, D.F.M. (2008) Fractional Optimal Control in the Sense of Caputo and the Fractional Noethers Theorem. International Mathematical Forum, 3, 479-493.

[7]   Warga, J. (1972) Optimal Control of Differential and Functional Equations. Academic Press, New York, 624с.

[8]   Pontreagin, L.S. (1980) Linear Differential Games of Pursuit. Sbornik Mathematics, 112, 307-330.

[9]   Mishchenko, E.F. and Satimov, N.Y. (1983) The Problem of Deviation from an Encounter in the Critical Case. Differential Equations, 19, 220-229.

[10]   Satimov, N.Y. (1976) On a Way to Avoid Contact in Differential Games. Sbornik Mathematics, 99, 380-393.

[11]   Satimov, N.Y. and Mamatov, M.Sh. (1990) On a Class of Linear Differential and Discrete Games between Groups of Pursuers and Evaders. Differential Equations, 26, 1541-1551.

[12]   Satimov, N.Y. and Tukhtasinov, M. (2005) On Some Game Problems in Controlled First-Order Evolutionary Equations. Differential Equations, 41, 1114-1121.

[13]   Mamatov, M.Sh. (2009) On the Theory of Differential Pursuit Games in Distributed Parameter Systems. Automatic Control and Computer Sciences, 43, 1-8.

[14]   Mamatov, M.Sh. and Alimov, H.N. (2013) Solution of the Problem of Persecution in Games Distributed Systems of Higher Order. Siberian Advances in Mathematics, Novosibirsk, 16, 229-239.

[15]   Mamatov, M.Sh. and Alimov, H.N. (2016) The Pursuit Problem Described by Differential Equations of Fractional Order. Proceedings of the 6th International Scientific Conference on European Applied Sciences: Challenges and Solutions, ORT Publishing, Stuttgart, 14-18.

[16]   Mamatov, M.Sh. and Alimov, H.N. (2016) By Solving the Problem of Harassment Described by Differential Equations of Fractional Order. Proceedings of the 7th International Scientific Conference on Theoretical and Applied Sciences in the USA, CIBUNET Publishing, New York, 6-10.

[17]   Mamatov, M.Sh., Durdiev, D.K. and Alimov, H.N. (2016) On the Theory of Fractional Order Differential Games of Pursuit. Journal of Applied Mathematics and Physics, 4, 1355-1362.
https://doi.org/10.4236/jamp.2016.48167

[18]   Mamatov, M.Sh., Durdiev, D.K. and Alimov, H.N. (2016) Fractional Integro-Differential Calculation and Its Appendices in the Theory of Differential Games of Prosecution of the Fractional Order. American Scientific Journal, 4, 72-77.

[19]   Mamatov, M.Sh., Tashmanov, E.B. and Alimov, H.N. (2013) Differential Games of Pursing in the Systems with Distributed Parameters and Geometrical Restrictions. American Journal of Computational Mathematics, 3, 56-61.

[20]   Mamatov, M.Sh., Tashmanov, E.B. and Alimov, H.N. (2015) Zwquasi Linear Discrete Games of Pursuit Described by High Order Equation Systems. Automatic Control and Computer Sciences, 49, 148-152.

 
 
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