منابع مشابه
Discrete-Time Fractional Optimal Control
Abstract: A formulation and solution of the discrete-time fractional optimal control problem in terms of the Caputo fractional derivative is presented in this paper. The performance index (PI) is considered in a quadratic form. The necessary and transversality conditions are obtained using a Hamiltonian approach. Both the free and fixed final state cases have been considered. Numerical examples...
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The theory of fractional calculus goes back to the beginning of the theory of di erential calculus but its inherent complexity postponed the application of the associated concepts. In the last decade the progress in the areas of chaos and fractals revealed subtle relationships with the fractional calculus leading to an increasing interest in the development of the new paradigm. In the area of a...
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We introduce a discrete-time fractional calculus of variations on the time scale hZ, h > 0. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that solutions to the considered fractional problems become the classical discrete-time solutions when the fractional order of ...
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Recent statistical literature has concerned with a study of long memory models which go beyond the presence of random walks and unit roots in the univariate time series processes. Following Mandelbrot and Van Ness (1968) fractional Brownian motion has been applied to “strongly dependent" geophysical phenomenon, McLeod and Hipel (1978). The objectives are threefold: (1) Explicitly account for pe...
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ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2011
ISSN: 1556-5068
DOI: 10.2139/ssrn.1896336