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Calculus of Variations on Time Scales and Discrete Fractional Calculus
We study problems of the calculus of variations and optimal control within
the framework of time scales. Specifically, we obtain Euler-Lagrange type
equations for both Lagrangians depending on higher order delta derivatives and
isoperimetric problems. We also develop some direct methods to solve certain
classes of variational problems via dynamic inequalities. In the last chapter
we introduce fractional difference operators and propose a new discrete-time
fractional calculus of variations. Corresponding Euler-Lagrange and Legendre
necessary optimality conditions are derived and some illustrative examples
provided.Comment: PhD thesis, University of Aveiro, 2010. Supervisor: Delfim F. M.
Torres; co-supervisor: Martin Bohner. Defended 26/July/201
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