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Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Author

Listed:
  • Fátima Cruz

    (Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
    These authors contributed equally to this work.)

  • Ricardo Almeida

    (Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
    These authors contributed equally to this work.)

  • Natália Martins

    (Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
    These authors contributed equally to this work.)

Abstract

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

Suggested Citation

  • Fátima Cruz & Ricardo Almeida & Natália Martins, 2021. "Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels," Mathematics, MDPI, vol. 9(14), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1665-:d:594925
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    References listed on IDEAS

    as
    1. Jozef Džurina & Said R. Grace & Irena Jadlovská & Tongxing Li, 2020. "Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 910-922, May.
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