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Finite Time Stability of Caputo–Katugampola Fractional Order Time Delay Projection Neural Networks

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Abstract

This paper explores the finite time stability of Caputo–Katugampola fractional order projection neural network with time delay. By employing the Sadovskii fixed point theorem, the Banach fixed point theorem and the generalized Gronwall inequality, we establish the existence and boundedness theorems of solutions for Caputo–Katugampola fractional order time delay projected neural networks. Further, we apply the proposed theorems and the techniques of inequalities to obtain the finite time stability of the equilibrium point for the presented system. Finally, the effectiveness of the theoretical result is shown through simulations for a numerical example.

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References

  1. Nagurney A, Zhang D (1995) Projected dynamical systems and variational inequalities with applications. Sci Bus Med 22:296

    MATH  Google Scholar 

  2. Brogliato B, Daniilidis A, Lemaréchal C, Acary V (2006) On the equivalence between complementarity systems, projected systems and differential inclusions. Syst Control Lett 55:45–51

    Article  MathSciNet  MATH  Google Scholar 

  3. Cojocaru MG, Daniele P, Nagurney A (2005) Projected dynamical systems and evolutionary variational inequalities via Hilbert spaces with applications. J Optim Theory Appl 127:549–563

    Article  MathSciNet  MATH  Google Scholar 

  4. Dupuis A, Nagurney A (1993) Dynamical systems and variational inequalities. Ann Oper Res 44:9–42

    Article  MathSciNet  MATH  Google Scholar 

  5. Hauswirth A, Bolognani S, Dorfler F (2021) Projected dynamical systems on irregular, non-Euclidean domains for nonlinear optimization. SIAM J Control Optim 59:635–668

    Article  MathSciNet  MATH  Google Scholar 

  6. Li JD, Huang NJ (2018) Asymptotical stability for a class of complex-valued projective neural network. J Optim Theory Appl 177:261–270

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang D, Nagurney A (1995) On the stability of projected dynamical systems. J Optim Theory Appl 85:97–124

    Article  MathSciNet  MATH  Google Scholar 

  8. Baleanu D (2012) Fractional calculus: models and numerical methods. World Scientific, Singapore

    Book  MATH  Google Scholar 

  9. Hilfer R (2000) Applications of fractional calculus in physics, applications of fractional calculus in physics. World Scientific, Singapore

    Book  MATH  Google Scholar 

  10. Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, Amsterdam

    MATH  Google Scholar 

  11. Podlubny I (1999) Fractional differential equations. Academic Press, San Diego

    MATH  Google Scholar 

  12. Wu ZB, Zou YZ (2014) Global fraction-order projective dynamical systems. Commun Nonlinear Sci 19:2811–2819

    Article  MathSciNet  MATH  Google Scholar 

  13. Wu ZB, Li JD, Huang NJ (2018) A new system of global fractional-order interval implicit projection neural networks. Neurocomputing 282:111–121

    Article  Google Scholar 

  14. Wu ZB, Min C, Huang NJ (2018) On a system of fuzzy fractional differential inclusions with projection operators. Fuzzy Sets Syst 347:70–88

    Article  MathSciNet  MATH  Google Scholar 

  15. Wu ZB, Zou YZ, Huang NJ (2016) A class of global fractional-order projective dynamical systems involving set-valued perturbations. Appl Math Comput 277:23–33

    MathSciNet  MATH  Google Scholar 

  16. Wu ZB, Zou YZ, Huang NJ (2016) A system of fractional-order interval projection neural networks. J Comput Appl Math 294:389–402

    Article  MathSciNet  MATH  Google Scholar 

  17. Wu ZB, Zou YZ, Huang NJ (2020) A new class of global fractional-order projective dynamical system with an application. J Ind Manag Optim 16:37–53

    Article  MathSciNet  MATH  Google Scholar 

  18. Li JD, Wu ZB, Huang NJ (2019) Asymptotical stability of Riemann–Liouville fractional-order neutral type delayed projective neural networks. Neural Proc Lett 50:565–579

    Article  Google Scholar 

  19. Huang WQ, Song QK, Zhao ZJ, Liu YR, Alsaadi FE (2021) Robust stability for a class of fractional-order complex-valued projective neural networks with neutral-type delays and uncertain parameters. Neurocomputing 450:399–410

    Article  Google Scholar 

  20. Li JD, Wu ZB, Huang NJ (2020) Global Mittag–Leffler stability of fractional-order projection neural networks with impulses. arXiv preprint arXiv:2011.0218

  21. Nagy AM, Makhlouf AB, Alsenafi A, Alazemi F (2021) Combination synchronization of fractional systems involving the Caputo–Hadamard derivative. Mathematics 9:2781

    Article  Google Scholar 

  22. Ben Makhlouf A (2018) Stability with respect to part of the variables of nonlinear Caputo fractional differential equations. Math Commun 23:119–126

    MathSciNet  MATH  Google Scholar 

  23. Ben Makhlouf A (2022) Partial practical stability for fractional-order nonlinear systems. Math Method Appl Sci. https://doi.org/10.1002/mma.8097

    Article  MathSciNet  MATH  Google Scholar 

  24. Zhang Y, Wu H, Cao JD (2020) Group consensus in finite time for fractional multiagent systems with discontinuous inherent dynamics subject to Hölder growth. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.3023704

    Article  Google Scholar 

  25. Wang X, Wu H, Cao JD (2020) Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth. Nonlinear Anal Hybrid Syst 37:100888

    Article  MathSciNet  MATH  Google Scholar 

  26. Li R, Wu H, Cao JD (2022) Impulsive exponential synchronization of fractional-order complex dynamical networks with derivative couplings via feedback control based on discrete time state observations. Acta Math Sci 42:737–754

    Article  MathSciNet  MATH  Google Scholar 

  27. Hien LV (2014) An explicit criterion for finite-time stability of linear nonautonomous systems with delays. Appl Math Lett 30:12–18

    Article  MathSciNet  MATH  Google Scholar 

  28. Cao XK, Wang JR (2018) Finite-time stability of a class of oscillating systems with two delays. Math Methods Appl Sci 41:4943–4954

    Article  MathSciNet  MATH  Google Scholar 

  29. Katugampola UN (2011) New approach to a generalized fractional integral. Appl Math Comput 218:860–865

    MathSciNet  MATH  Google Scholar 

  30. Katugampola UN (2014) Existence and uniqueness results for a class of generalized fractional differential equations. arXiv Preprint arXiv:1411.5229

  31. Anderson DR, Ulness DJ (2016) Properties of the Katugampola fractional derivative with potential application in quantum mechanics. J Math Phys 56:063502

    Article  MathSciNet  MATH  Google Scholar 

  32. Cavazzuti E, Pappalardo M, Passacantando M (2002) Nash equilibria, variational inequalities, and dynamical systems. J Optim Theory Appl 114:491–506

    Article  MathSciNet  MATH  Google Scholar 

  33. Pappalardo M, Passacantando M (2002) Stability for equilibrium problems: from variational inequalities to dynamical systems. J Optim Theory Appl 113:567–582

    Article  MathSciNet  MATH  Google Scholar 

  34. Xia Y, Leung H, Wang J (2002) A projection neural network and its application to constrained optimization problems. IEEE Trans Circuits Syst I Reg 49:447–458

    Article  MathSciNet  MATH  Google Scholar 

  35. Katugampola UN (2014) A new approach to generalized fractional derivatives. Bull Math Anal Appl 6:1–15

    MathSciNet  MATH  Google Scholar 

  36. Kinderlehrer D, Stampacchia G (1980) An introduction to variational inequalities and their applications. Academic Press, New York

    MATH  Google Scholar 

  37. Sousa JVC, Oliveira EC (2017) A Gronwall inequality and the Cauchy-type problem by means of \(\Psi \)-Hilfer operator. arXiv preprint arXiv:1709.03634

  38. Ke Y, Miao C (2015) Stability analysis of fractional-order Cohen–Grossberg neural networks with time delay. Int J Comput Math 92:1102–1113

    Article  MathSciNet  MATH  Google Scholar 

  39. Kamenskii M, Obukhovskii V, Zecca P (2001) Condensing multivaluedmaps and semilinear differential inclusions in Banach spaces. de Gruyter, Berlin

    Book  MATH  Google Scholar 

  40. Sadvskii BN (1967) A fixed point principle. Funct Anal Appl 1:151–513

    Article  MathSciNet  Google Scholar 

  41. Zhao W, Wu H (2018) Fixed-time synchronization of semi-Markovian jumping neural networks with time-varying delays. Adv Differ Equ 1:1–21

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. College of Science, Guilin University of Technology, Guilin, Guangxi, 541004, People’s Republic of China

    Mengxue Dai, Yirong Jiang & Jinsheng Du

  2. School of Mathematics and Physics, Guangxi University for Nationalities, Nanning, Guangxi, 530006, People’s Republic of China

    Guoji Tang

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  1. Mengxue Dai
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  2. Yirong Jiang
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  3. Jinsheng Du
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  4. Guoji Tang
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Correspondence to Yirong Jiang.

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This work was supported by the the National Natural Science Foundation of China (11961006, 12161028), Natural Science Foundation of Guangxi Province (2018GXNSFAA281021,2020GXNSFAA159100), Guangxi Science and Technology Base Foundation(AD20159017) and the Foundation of Guilin University of Technology (GUTQDJJ2017062)

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Dai, M., Jiang, Y., Du, J. et al. Finite Time Stability of Caputo–Katugampola Fractional Order Time Delay Projection Neural Networks. Neural Process Lett 54, 4851–4867 (2022). https://doi.org/10.1007/s11063-022-10838-1

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