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Composition Functionals in Fractional Calculus of Variations
Optimization and Control · Submitted 14 Sep 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We prove Euler-Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals.
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The abstract, sentence by sentence
We prove Euler-Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. As an application, we get optimality conditions for the product and the quotient of fractional variational functionals.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We prove Euler-Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals. | contribution 0.54 | 0.96 | 0.88 | asserted 1.00 |
| s1 | Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. | method 1.00 | 0.28 | 0.04 | asserted 0.99 |
| s2 | As an application, we get optimality conditions for the product and the quotient of fractional variational functionals. | result 0.89 | 0.95 | 0.20 | asserted 1.00 |
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The paper
Original abstract
We prove Euler-Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. As an application, we get optimality conditions for the product and the quotient of fractional variational functionals.
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How the literature uses it
6 arXiv papers cite this in 9 sentences
Papers citing it · 2 sentences without a confident label
Builds on it 1 paper
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In the present paper we develop further the theory initiated by Jumarie in 2009 [ref] , by considering other fundamental problems of variational type than those treated before in [ref] .
Fractional variational calculus for nondifferentiable functions · Comparison with previous results in the literature · 1.00
Compares with it 1 paper
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Results available in the literature reduce to those in [ref] (published in 2009) and [ref] (published in 2010).
Fractional variational calculus for nondifferentiable functions · Comparison with previous results in the literature · 0.88
Cites it as background 4 papers
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Roughly speaking, available results in the literature use different notions of fractional derivatives, in the sense of Riemann–Liouville [ref] , Caputo [ref] , Riesz [ref] , combined fractional derivatives [ref] , or modified/generalized versions of the classical fractional operators [ref] , in order to describe different variational principles.
Generalized fractional calculus with applications to the calculus of variations · Introduction · 0.97
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For more information on the subject we refer the reader to [ref] .
Fractional Calculus of Variations for Double Integrals · Preliminaries · 0.99
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Investigations cover problems depending on the Riemann-Liouville fractional derivative (see, e.g., [ref] ), the Caputo fractional derivative (see, e.g., [ref] ), and others [ref] .
A formulation of the fractional Noether-type theorem for multidimensional Lagrangians · Introduction · 0.94
What it cites · 3 sentences without a confident label
Cites as background 11 papers
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Investigations cover problems depending on Riemann–Liouville fractional derivatives (see, e.g., [ref] ), the Caputo fractional derivative (see, e.g., [ref] ), the symmetric fractional derivative (see, e.g., [ref] ), the Jumarie fractional derivative (see, e.g., [ref] ), and others [ref] .
Fractional conservation laws in optimal control theory · Introduction · 0.99
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Investigations cover problems depending on Riemann–Liouville fractional derivatives (see, e.g., [ref] ), the Caputo fractional derivative (see, e.g., [ref] ), the symmetric fractional derivative (see, e.g., [ref] ), the Jumarie fractional derivative (see, e.g., [ref] ), and others [ref] .
Fractional Action-Like Variational Problems · Introduction · 0.99
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Investigations cover problems depending on Riemann–Liouville fractional derivatives (see, e.g., [ref] ), the Caputo fractional derivative (see, e.g., [ref] ), the symmetric fractional derivative (see, e.g., [ref] ), the Jumarie fractional derivative (see, e.g., [ref] ), and others [ref] .
Constants of Motion for Non-Differentiable Quantum Variational Problems · Introduction · 0.99
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