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Variational Problems Involving a Caputo-Type Fractional Derivative

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  • Ricardo Almeida

    (University of Aveiro)

Abstract

The aim of this paper is to study certain problems of calculus of variations that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo–Hadamard fractional derivatives that are dependent on a real parameter $$\rho $$ ρ . Sufficient and necessary conditions of the first and second order are presented. The cases of integral and holonomic constraints are also considered.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-016-0883-4
    DOI: 10.1007/s10957-016-0883-4
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    Cited by:

    1. 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.
    2. Harendra Singh & Rajesh K. Pandey & Hari Mohan Srivastava, 2019. "Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials," Mathematics, MDPI, vol. 7(3), pages 1-24, February.
    3. Muath Awadalla & Kinda Abuasbeh & Muthaiah Subramanian & Murugesan Manigandan, 2022. "On a System of ψ -Caputo Hybrid Fractional Differential Equations with Dirichlet Boundary Conditions," Mathematics, MDPI, vol. 10(10), pages 1-15, May.
    4. 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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