The Legendre condition of the fractional calculus of variations

DOI10.1080/02331934.2013.877908zbMath1297.26014arXiv1312.4714OpenAlexW2083118792WikidataQ57650744 ScholiaQ57650744MaRDI QIDQ5495580

Delfim F. M. Torres, Matheus Jatkoske Lazo

Publication date: 5 August 2014

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.4714

zbMATH Keywords

fractional calculusCaputo derivativesecond-order optimality conditionRiemann-Liouville derivativeLegendre conditioncalculus of variations and optimal control

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Optimality conditions for free problems in one independent variable (49K05)

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Variational problems with partial fractional derivative: optimal conditions and Noether's theorem ⋮ Variational problems involving a Caputo-type fractional derivative ⋮ Optimality conditions for fractional variational problems with free terminal time ⋮ Legendre's necessary condition for fractional Bolza functionals with mixed initial/final constraints ⋮ Analysis and numerical approximation of tempered fractional calculus of variations problems ⋮ Fractional systems and optimization ⋮ The Euler-Lagrange and Legendre equations for functionals involving distributed-order fractional derivatives ⋮ A highly accurate collocation algorithm for 1 + 1 and 2 + 1 fractional percolation equations

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