# Hamilton’s Principle with Variable Order Fractional Derivatives

• Volume: 14, Issue: 1, page 94-109
• ISSN: 1311-0454

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## Abstract

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

## How to cite

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Atanackovic, Teodor, and Pilipovic, Stevan. "Hamilton’s Principle with Variable Order Fractional Derivatives." Fractional Calculus and Applied Analysis 14.1 (2011): 94-109. <http://eudml.org/doc/219655>.

@article{Atanackovic2011,
abstract = {MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe 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.},
author = {Atanackovic, Teodor, Pilipovic, Stevan},
journal = {Fractional Calculus and Applied Analysis},
keywords = {Variable Order Fractional Derivative; Variational Principle of Hamilton’s Type; variable order fractional derivative variational principle of Hamilton's type},
language = {eng},
number = {1},
pages = {94-109},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Hamilton’s Principle with Variable Order Fractional Derivatives},
url = {http://eudml.org/doc/219655},
volume = {14},
year = {2011},
}

TY - JOUR
AU - Atanackovic, Teodor
AU - Pilipovic, Stevan
TI - Hamilton’s Principle with Variable Order Fractional Derivatives
JO - Fractional Calculus and Applied Analysis
PY - 2011
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 14
IS - 1
SP - 94
EP - 109
AB - MSC 2010: 26A33, 70H25, 46F12, 34K37 Dedicated to 80-th birthday of Prof. Rudolf GorenfloWe 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.
LA - eng
KW - Variable Order Fractional Derivative; Variational Principle of Hamilton’s Type; variable order fractional derivative variational principle of Hamilton's type
UR - http://eudml.org/doc/219655
ER -

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