Necessary Optimality Conditions for Fractional Difference Problems of the Calculus of Variations
| Autor: | Delfim F. M. Torres, Nuno R. O. Bastos, Rui A. C. Ferreira |
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| Jazyk: | angličtina |
| Rok vydání: | 2010 |
| Předmět: |
Applied Mathematics
010102 general mathematics Type (model theory) 01 natural sciences Fractional calculus 010101 applied mathematics Euler–Lagrange equation 49K05 39A12 26A33 Optimization and Control (math.OC) FOS: Mathematics Discrete Mathematics and Combinatorics Applied mathematics Order (group theory) Calculus of variations 0101 mathematics Legendre polynomials Mathematics - Optimization and Control Analysis Mathematics |
| Popis: | We introduce a discrete-time fractional calculus of variations. 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 the solutions of the fractional problems coincide with the solutions of the corresponding non-fractional variational problems when the order of the discrete derivatives is an integer value. Submitted 09-May-2009 to Discrete and Continuous Dynamical Systems (DCDS-B); revised 27-March-2010; accepted 04-July-2010 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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