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Discrete-time fractional variational problems
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DOI：10.1016/j.sigpro.2010.05.001.png)
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摘要
En 中文
We introduce a discrete-time fractional calculus of variations on the time scale (hZ)(a), a is an element of R,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 the discrete-derivatives are integer values, and that they converge to the fractional continuous-time solutions when h tends to zero. Our Legendre type condition is useful to eliminate false candidates identified via the Euler-Lagrange fractional equation. (C) 2010 Elsevier B.V. All rights reserved.
Keyword:
Fractional difference calculus
Calculus of variations
Fractional summation by parts
Euler-Lagrange equation
Natural boundary conditions
Legendre necessary condition
Time scale hZ
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3.6
论文数:
10.0K
被引数:
1.7W
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