Journal
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
Volume 14, Issue 1, Pages 94-109Publisher
VERSITA
DOI: 10.2478/s13540-011-0007-7
Keywords
variable order fractional derivative; variational principle of Hamilton's type
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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.
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