Geodesic
Hamilton’s Principle with Variable Order Fractional Derivatives
Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 94-109.

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We propose a generalization of Hamilton’s principle in which the minimization is performed with respect to the admissible functions and the order of the derivation. The Euler–Lagrange equations for such minimization are derived. They generalize the classical Euler-Lagrange equation. Also, a new variational problem is formulated in the case when the order of the derivative is defined through a constitutive equation. Necessary conditions for the existence of the minimizer are obtained. They imply various known results in a special cases.
Keywords: Variable Order Fractional Derivative, Variational Principle of Hamilton’s Type 
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Atanackovic, Teodor; Pilipovic, Stevan. Hamilton’s Principle with Variable Order Fractional Derivatives. Fractional calculus and applied analysis, Tome 14 (2011) no. 1, pp. 94-109. http://geodesic.mathdoc.fr/item/FCAA_2011_14_1_a5/