Discrete-time fractional variational problems

Authors:
Nuno R. O. Bastos;Rui A. C. Ferreira;Delfim F. M. Torres
Affiliations:
Department of Mathematics, ESTGV, Polytechnic Institute of Viseu, 3504-510 Viseu, Portugal;Faculty of Engineering and Natural Sciences, Lusophone University of Humanities and Technologies, 1749-024 Lisbon, Portugal;Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
Venue:
Signal Processing
Year:
2011

Citing 2
Cited 8

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Abstract

We introduce a discrete-time fractional calculus of variations on the time scale (hZ)"a,a@?R,h0. 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.