Discrete-time fractional variational problems
| Autor: | Nuno R. O. Bastos, Delfim F. M. Torres, Rui A. C. Ferreira |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
26A33
39A12 49K05 010102 general mathematics Mathematical analysis Zero (complex analysis) Type (model theory) 01 natural sciences Fractional calculus 010101 applied mathematics Euler–Lagrange equation Fractional programming Discrete time and continuous time Optimization and Control (math.OC) Control and Systems Engineering Signal Processing FOS: Mathematics Computer Vision and Pattern Recognition Calculus of variations 0101 mathematics Electrical and Electronic Engineering Mathematics - Optimization and Control Legendre polynomials Software Mathematics |
| Zdroj: | Signal Processing. 91:513-524 |
| ISSN: | 0165-1684 |
| DOI: | 10.1016/j.sigpro.2010.05.001 |
| Popis: | We introduce a discrete-time fractional calculus of variations on the time scale $h\mathbb{Z}$, $h > 0$. 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. Submitted 24/Nov/2009; Revised 16/Mar/2010; Accepted 3/May/2010; for publication in Signal Processing. |
| Databáze: | OpenAIRE |
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