Calculus of Variations on Time Scales and Discrete Fractional Calculus

Details Calculus of Variations on Time Scales and Discrete Fractional Calculus Calculus of Variations on Time Scales and Discrete Fractional Calculus

2010-07-28

arxiv.org/abs/1007.5087v1

University of Aveiro, PhD thesis, 2010

Mathematics

Optimization and Control

PhD thesis, University of Aveiro, 2010. Supervisor: Delfim F. M. Torres; co-supervisor: Martin Bohner. Defended 26/July/2010

Scientific paper

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.

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