Variational Problems with Fractional Derivatives: Euler-Lagrange Equations

Abstract

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.

References in corpus (2)

• Fractional Calculus: Integral and Differential Equations of Fractional Order
• A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations

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