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The Euler–Lagrange and Legendre equations for functionals involving distributed–order fractional derivatives

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  • Almeida, Ricardo
  • Morgado, M. Luísa

Abstract

In this paper, we extend some fractional calculus of variations results by considering functionals depending on distributed–order fractional derivatives. Using variational techniques, we deduce optimal necessary conditions of Euler–Lagrange and Legendre type. We also study the case where integral and holonomic constraints are imposed. Finally, a numerical procedure is given to solve some proposed problems.

Suggested Citation

  • Almeida, Ricardo & Morgado, M. Luísa, 2018. "The Euler–Lagrange and Legendre equations for functionals involving distributed–order fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 394-403.
    • Handle: RePEc:eee:apmaco:v:331:y:2018:i:c:p:394-403
    DOI: 10.1016/j.amc.2018.03.022
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    References listed on IDEAS

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    1. Ricardo Almeida, 2017. "Variational Problems Involving a Caputo-Type Fractional Derivative," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 276-294, July.
    2. Liang, Yingjie & Chen, Wen & Magin, Richard L., 2016. "Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 327-335.
    3. Mijena, Jebessa B. & Nane, Erkan, 2014. "Correlation structure of time-changed Pearson diffusions," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 68-77.
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    Cited by:

    1. Faïçal Ndaïrou & Delfim F. M. Torres, 2021. "Pontryagin Maximum Principle for Distributed-Order Fractional Systems," Mathematics, MDPI, vol. 9(16), pages 1-12, August.
    2. Loïc Bourdin & Rui A. C. Ferreira, 2021. "Legendre’s Necessary Condition for Fractional Bolza Functionals with Mixed Initial/Final Constraints," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 672-708, August.

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