Optimal control of fractional diffusion equation

作者：Mophou Gisele M^*

来源：Computers & Mathematics with Applications, 2011, 61(1): 68-78.

DOI：10.1016/j.camwa.2010.10.030

• Fractional differential equation
• Laplace transform
• Optimal control

In this paper we apply the classical control theory to a fractional diffusion equation in a bounded domain. The fractional time derivative is considered in a Riemann-Liouville sense. We first study the existence and the uniqueness of the solution of the fractional diffusion equation in a Hilbert space. Then we show that the considered optimal control problem 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 for the optimal control.

• 出版日期2011-1