# Hamilton’s Principle with Variable Order Fractional Derivatives

Atanackovic, Teodor; Pilipovic, Stevan

Fractional Calculus and Applied Analysis (2011)

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

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topAtanackovic, 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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