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Fixed Point Theorem and Fractional Differential Equations with Multiple Delays Related with Chaos Neuron Models

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DOI: 10.4236/am.2015.613192    2,747 Downloads   3,295 Views   Citations

ABSTRACT

In this paper, we show a fixed point theorem which deduces to both of Lou’s fixed point theorem and de Pascale and de Pascale’s fixed point theorem. Moreover, our result can be applied to show the existence and uniqueness of solutions for fractional differential equations with multiple delays. Using the theorem, we discuss the fractional chaos neuron model.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Kawasaki, T. and Toyoda, M. (2015) Fixed Point Theorem and Fractional Differential Equations with Multiple Delays Related with Chaos Neuron Models. Applied Mathematics, 6, 2192-2198. doi: 10.4236/am.2015.613192.

References

[1] Banach, S. (1922) Sur les opérations dans les ensembles abstraits et leur application aux équations integrals. Fundamenta Mathematicae, 3, 133-181.
[2] Lou, B. (1999) Fixed Points for Operators in a Space of Continuous Functions and Applications. Proceedings of the American Mathematical Society, 127, 1159-2264.
http://dx.doi.org/10.1090/S0002-9939-99-05211-9
[3] de Pascale, E. and de Pascale, L. (2002) Fixed Points for Some Non-Obviously Contractive Operators. Proceedings of the American Mathematical Society, 130, 3249-3254.
http://dx.doi.org/10.1090/S0002-9939-02-06704-7
[4] Matsuzaki, T. and Nakagawa, M. (2003) A Chaos Neuron Model with Fractional Differential Equation. Journal of the Physical Society of Japan, 72, 2678-2684.
http://dx.doi.org/10.1143/JPSJ.72.2678
[5] Suzuki, T. (2006) Lou’s Fixed Point Theorem in a Space of Continuous Mappings. Journal of the Mathematical Society of Japan, 58, 769-774.
http://dx.doi.org/10.2969/jmsj/1156342037
[6] Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006) Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam.
[7] Lai, X. and Zhang, Y. (2012) Fixed Point and Asymptotic Analysis of Cellular Neural Networks. Journal of Applied Mathematics, 2012, Article ID: 689845.
[8] Zhang, Y. and Luo, Q. (2013) Global Exponential Stability of Impulsive Cellular Neural Networks with Time-Varying Delays via Fixed Point Theory. Advances in Difference Equations, 2013, 2013:23.

  
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