Optimal Control of a Fractional Diffusion Equation with Delay

Authors

  • Gisèle Mophou Université des Antilles et de la Guyane
  • J. M. Fotsing Université des Antilles et de la Guyane, Institut d’Enseignement Supérieur de la Guyane

DOI:

https://doi.org/10.24297/jam.v6i3.7244

Keywords:

fractional differential equation, optimal control

Abstract

We study a homogeneous Dirichlet boundary fractional diffusion equation with delay in a bounded domain. The fractional time derivative is considered in the left Caputo sense. By means of a linear continuous operator, we first transform the fractional diffusion equation with delay into a an equivalent equation without delay. Then we show that the optimal control problem associate to the controlled equivalent fractional diffusion equation has a unique solution. Interpreting the Euler-Lagrange first order optimality condition with an adjoint problem defined by means of right fractional Caputo derivative, we obtain an optimality system.

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Author Biographies

Gisèle Mophou, Université des Antilles et de la Guyane

Gisèle M. Mophou, Laboratoire CEREGMIA, Université des Antilles et de la Guyane, Campus Fouillole,
97159 Pointe-à-Pitre Guadeloupe (FWI).

J. M. Fotsing, Université des Antilles et de la Guyane, Institut d’Enseignement Supérieur de la Guyane

Jean-Marie Fotsing, Laboratoire CEREGMIA, Université des Antilles et de la Guyane, Institut
d’Enseignement Supérieur de la Guyane, 2091 Route de Baduel 97337 Cayenne, Guyane

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Published

2014-02-20

How to Cite

Mophou, G., & Fotsing, J. M. (2014). Optimal Control of a Fractional Diffusion Equation with Delay. JOURNAL OF ADVANCES IN MATHEMATICS, 6(3), 1017–1031. https://doi.org/10.24297/jam.v6i3.7244

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Articles