Optimal Control of a Fractional Diffusion Equation with Delay
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2014, Vol 6, Issue 3
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.
Authors and Affiliations
Gisèle Mophou, J. M. Fotsing
Keywords
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- EP ID EP651243
- DOI 10.24297/jam.v6i3.7244
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