Fractional Calculus on Time Scales

Nuno R. O. Bastos

Fractional Calculus on Time Scales

Classical Analysis and ODEs 2012-02-15 v1 Optimization and Control

Authors: Nuno R. O. Bastos

Abstract

We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$ . First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. We also give new definitions of fractional derivatives and integrals on time scales via the inverse generalized Laplace transform.

Keywords

calculus of variations fractional calculus fractional differential equations

Cite

@article{arxiv.1202.2960,
  title  = {Fractional Calculus on Time Scales},
  author = {Nuno R. O. Bastos},
  journal= {arXiv preprint arXiv:1202.2960},
  year   = {2012}
}

Comments

PhD thesis, Doctoral Programme in Mathematics and Applications (PDMA), University of Aveiro and University of Minho, 2012. Supervisor: Delfim F. M. Torres. Defended and approved 13/Feb/2012

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