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Part of the book series: Fundamental Theories of Physics ((FTPH,volume 112))

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Abstract

The ultimate purpose of any theory is to provide new approaches to practical problems, and in the present chapter we shall outline some applications of the above results. Analysis of the stochastic stability of dynamical systems, the theory of time series of fractional order, fractals in image processing, solution of the master equation, definition of the master equation of fractional order, optimal control of dynamical systems subject to complex-valued fractional Brownian motion motion, fractals in human systems, the relation between dynamics of information and fractals.

Physical models are as different from the world as a geographical map is from the surface of the earth.

Léon Brillouin

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References

  1. BOX, G.E.P. and JENKINS, G.M. Time Series Analysis. Forecasting and Control, Holden-Day, San Francisco, 1970

    MATH  Google Scholar 

  2. BROCKVWELL, P.J. and DAVIS, R.A.; Time Series. Theoriy and Method, Springer, 1987, Berlin

    Google Scholar 

  3. CONNES, A.; Noncommutative geometry, Academic press, New York, 1994

    MATH  Google Scholar 

  4. DYNKIN, E.B.; Controlled random sequences, Theory of Probability and its Applications, Vol 10, pp 1–14, 1965

    Article  MathSciNet  Google Scholar 

  5. ELWAKIL, S.A. and ZAHRAN, M.A.; Fractional integral representation of master equations, Chaos, Solitons and Fractals, Vol 10, No 8, pp 1309–1313, 1999

    Article  MathSciNet  Google Scholar 

  6. JUMARIE, G.; A practical variational approach to stochastic optimal control via state moment equations, Journal of Franklin Institute: Engineering and Applied Mathematics, Vol 332 B, No 6, pp 761–772, 1995

    MathSciNet  Google Scholar 

  7. JUMARIE, G.; Improvement of stochastic neighbouring optimal control, using nonlinear Gaussian white noise terms in the Taylor expansions, J. of Franklin Institute: Engineering and Applied Mathematics, Vol 333 B, No 5, pp 773–789, 1966

    Google Scholar 

  8. JUMARIE, G.; Stochastic dynamics and fractional white noise in the complex plane. Stability, entropy and fractal dimension, Systems Analysis, Modelling, Simulation, Vol 134, pp 307–334, 1999

    Google Scholar 

  9. KATS. I.I. and KRASOVSKII, N.N.; On the stability of systems with random disturbances, J. Applied Mathematics and Mechanics (PMM), Vol 24, pp 65–71, 1960

    Google Scholar 

  10. KUSHNER, H.J.; Stochastic Stability and Control, Academic Press, New-York, 1967

    MATH  Google Scholar 

  11. MANDELBROT, B.B.; Fractals and Scaling in Finance. Discontinuity, Concentration, Risk, Springer Verlag, New York, 1997

    Book  Google Scholar 

  12. NOTTALE, L.; Fractal-Space Time and Microphysics, World Scientific, Singapour, 1993

    MATH  Google Scholar 

  13. STEINGEL, R.; Stochastic Optimal Control, Wiley, New York, 1986

    Google Scholar 

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© 2000 Springer Science+Business Media Dordrecht

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Jumarie, G. (2000). Outline of Applications. In: Maximum Entropy, Information Without Probability and Complex Fractals. Fundamental Theories of Physics, vol 112. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9496-7_10

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  • DOI: https://doi.org/10.1007/978-94-015-9496-7_10

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5467-8

  • Online ISBN: 978-94-015-9496-7

  • eBook Packages: Springer Book Archive

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