Optimal Control of a Fractional Diffusion Equation with Delay
DOI:
https://doi.org/10.24297/jam.v6i3.7244Keywords:
fractional differential equation, optimal controlAbstract
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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