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Optimal Control of Diffusion Equation with Fractional Time Derivative with Nonlocal and Nonsingular Mittag-Leffler Kernel

Author

Listed:
  • Jean-Daniel Djida

    (Universidade de Santiago de Compostela
    African Institute for Mathematical Sciences (AIMS))

  • Gisèle Mophou

    (African Institute for Mathematical Sciences (AIMS)
    Université des Antilles)

  • Iván Area

    (Universidade de Vigo)

Abstract

In this paper, we consider a diffusion equation with fractional time derivative with nonsingular Mittag-Leffler kernel in Hilbert spaces. We first prove the existence and uniqueness of solution by means of a spectral argument. Then, we consider a distributed controlled fractional diffusion problem. We show that there exists a unique optimal control, which can act on the system in order to approach the state of the system by a given state at minimal cost. Finally, using the Euler–Lagrange first-order optimality condition, we obtain an optimality system, which characterizes the optimal control.

Suggested Citation

  • Jean-Daniel Djida & Gisèle Mophou & Iván Area, 2019. "Optimal Control of Diffusion Equation with Fractional Time Derivative with Nonlocal and Nonsingular Mittag-Leffler Kernel," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 540-557, August.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:2:d:10.1007_s10957-018-1305-6
    DOI: 10.1007/s10957-018-1305-6
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    Cited by:

    1. Balasubramaniam, P., 2022. "Solvability of Atangana-Baleanu-Riemann (ABR) fractional stochastic differential equations driven by Rosenblatt process via measure of noncompactness," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    2. Balasubramaniam, P., 2021. "Controllability of semilinear noninstantaneous impulsive ABC neutral fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Kottakkaran Sooppy Nisar, 2019. "Fractional Integrations of a Generalized Mittag-Leffler Type Function and Its Application," Mathematics, MDPI, vol. 7(12), pages 1-13, December.

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