Abstract
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.
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Dedicated to 80-th birthday of Prof. Rudolf Gorenflo
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Atanackovic, T.M., Pilipovic, S. Hamilton’s principle with variable order fractional derivatives. fcaa 14, 94–109 (2011). https://doi.org/10.2478/s13540-011-0007-7
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DOI: https://doi.org/10.2478/s13540-011-0007-7