, Volume 69, Issue 3, pp 977-982
Date: 18 Jan 2012

Fractional Euler–Lagrange equations revisited

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Abstract

This paper presents the necessary and sufficient optimality conditions for the Euler–Lagrange fractional equations of fractional variational problems with determining in which spaces the functional must exist where the functional contains right and left fractional derivatives in the Riemann–Liouville sense and the upper bound of integration less than the upper bound of the interval of the fractional derivative. In order to illustrate our results, one example is presented.