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Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels

Author

Listed:
  • Faïçal Ndaïrou

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

  • Delfim F. M. Torres

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

Abstract

Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall type inequality as well as results on continuity and differentiability of perturbed trajectories. Moreover, a Mangasarian type sufficient global optimality condition for the general analytic kernel fractional optimal control problem is proved. An illustrative example is discussed.

Suggested Citation

  • Faïçal Ndaïrou & Delfim F. M. Torres, 2021. "Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels," Mathematics, MDPI, vol. 9(19), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2355-:d:640823
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    References listed on IDEAS

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    1. Fernandez, Arran & Özarslan, Mehmet Ali & Baleanu, Dumitru, 2019. "On fractional calculus with general analytic kernels," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 248-265.
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