Variational Problems with Fractional Derivatives: Euler-Lagrange Equations

Details Variational Problems with Fractional Derivatives: Euler-Lagrange Equations Variational Problems with Fractional Derivatives: Euler-Lagrange Equations

2011-01-15

arxiv.org/abs/1101.2961v1

J. Phys A: Math. Theor., 41, 095201, 2008

Mathematics

Functional Analysis

Scientific paper

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these two bounds coincide, we derive a new form of Euler-Lagrange equations. We use approximations for fractional derivatives in the Lagrangian and obtain the Euler-Lagrange equations which approximate the initial Euler-Lagrange equations in a weak sense.

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