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Hamilton’s Principle with Variable Order Fractional Derivatives

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Authors: Atanackovic, TeodorPilipovic, Stevan
Issue Date: 2011
Citation: Fractional Calculus and Applied Analysis, Vol. 14, No 1, (2011), 94p-109p Copy to clipboard
ISSN: 1311-0454
URI: http://hdl.handle.net/10525/1684 Copy to clipboard
Note:

MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo

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.
Language: en
Publisher: Institute of Mathematics and Informatics, Bulgarian Academy of SciencesSubject: Variable Order Fractional DerivativeVariational Principle of Hamilton’s Type
Type: Article