Necessary optimality conditions for fractional action‐like integrals of variational calculus with Riemann–Liouville derivatives of order (α, β)

By Rami Ahmad El-Nabulsi, Delfim F. M. Torres. 2007

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We derive Euler–Lagrange‐type equations for fractional action‐like integrals of the calculus of variations which depend on the Riemann–Liouville derivatives of order (α, β), α>0, β>0, recently introduced by Cresson. Some interesting consequences are obtained and discussed. Copyright © 2007 John Wiley & Sons, Ltd.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/bc7efaba3da3c10c7ba7c35910df2654fca1ac93

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Fractional Optimal Control Problems with Several State and Control Variables (2010, unknown): “…and Klafter, 2000 Agrawal, 2001 Tenreiro-Machado, 2001 Agrawal, 2002 Agrawal et al., 2004 Agrawal, 2005 Baleanu and Muslih, 2005 Muslih and Baleanu, 2005 Baleanu et al., 2006 Magin, 2006 Agrawal, 2007a,b El-Nabulsi and Torres, 2007 Rabei et al., 2007 Vinagre and Feliu, 2007 Tricaud and Chen, 2008).”
Fractional actionlike variational problems (2008, methodology): “ote that for γ = i one has Dα,β γ = −D β t−; for γ = −i, Dα,β γ = Dα a+; for α → 1 and β → 1 one obtains Dα,β γ = d dt and (3) is reduced to the classical functional of the calculus of variations. In [14] it is proved that the FELE correspondent to (3) is given by ∂L ∂q −Dβ,α −γ ∂L ∂q˙ = 1−α t− τ ”
NECESSARY OPTIMALITY CONDITIONS FOR FRACTIONAL DIFFERENCE PROBLEMS OF THE CALCULUS OF VARIATIONS (2010, background): “The study of fractional problems of the Calculus of Variations and respective Euler-Lagrange equations is a fairly recent issue – see [1, 2, 5, 7, 8, 11, 13, 15, 16, 21] and references therein – and include only the continuous case.”
Fractional Optimal Control in the Sense of Caputo and the Fractional Noether's Theorem (2007, methodology): “Similar operators were used in [11] and [13, Def.”