Cosmological Models with Fractional Derivatives and Fractional Action Functional

Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both cases is given.Comment: 14 page

A formulation of the fractional Noether-type theorem for multidimensional Lagrangians

This paper presents the Euler-Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses well-known notion of the Riemann-Liouville fractional derivative.Comment: Submitted 26-SEP-2011; accepted 3-MAR-2012; for publication in Applied Mathematics Letter

Noether's Theorem for Fractional Optimal Control Problems

We begin by reporting on some recent results of the authors (Frederico and Torres, 2006), concerning the use of the fractional Euler-Lagrange notion to prove a Noether-like theorem for the problems of the calculus of variations with fractional derivatives. We then obtain, following the Lagrange multiplier technique used in (Agrawal, 2004), a new version of Noether's theorem to fractional optimal control systems.Comment: To be presented at FDA'06 - 2nd IFAC Workshop on Fractional Differentiation and its Applications, 19-21 July 2006, Porto, Portugal. Accepted (07-March-2006) for the Conference Proceeding

Fractional Noether's theorem in the Riesz-Caputo sense

We prove a Noether's theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.Comment: Accepted (25/Jan/2010) for publication in Applied Mathematics and Computatio

Primjena dijelnog učinu-sličnog varijacijskog načela za rast crnih jama i energiju skupljanja

Some interesting aspects and features of black hole growth and accretion energy rather than evaporation are discussed within the framework of fractional action-like variational approach recently introduced by the author.U okviru dijelnog učinu-sličnog varijacijskog načela, nedavno uvedenog ovim autorom, raspravljaju se neki zanimljivi izgledi i odlike rasta crnih jama i energije skupljanja, umjesto isparavanja crnih jama

Izmijenjena Gauss-Bonnet-Brans-Dickeova kozmologija sa zamrznutim skalarnim potencijalima

In this letter, we discuss the late-time dynamics of a modified Gauss-Bonnet gravity theory `a la Brans-Dicke, dominated by freezing potentials V (φ) ∝ φ −n, n ∈ R. For a certain choice of the parameter n, it is observed that the universe is dominated by dark energy, accelerated in time and controlled by the Gauss-Bonnet invariant term. Besides, the Brans-Dicke parameter ω ≫ 1 compatible with some recent reports where this bound is updated by several thousands following from the bound on “˜γ − 1” from the Cassini mission, ˜γ being the PPN parameter. Many additional interesting features are raised and discussed in some details.Razmatramo kasnovremensku dinamiku izmijenjene Gauss-Bonnetove gravitacijske teorije u kojoj prevladavaju zamrznuti skalarni potencijali V (φ) ∝ φ −n, n ∈ R. Primjećuje se kako za neki izbor parametra n u svemiru prevladava tamna tvar, ubrzana u vremenu i upravljana Gauss-Bonnetovim invarijantnim članom. K tome je Brans-Dickeov parametar ω ≫ 1 u skladu s nedavnim izvješćima gdje je ta granica obnovljena više tisuća puta na osnovi granice za “γ˜ − 1” određene sondom Cassini, gdje je ˜γ PNP parametar. Više drugih pitanja se postavlja i podrobno raspravlja