The Wright functions as solutions of the time-fractional diffusion equation
Applied Mathematics and Computation - Special issue: Advanced special functions and related topics in differential equations, third Melfi workshop, proceedings of the Melfi school on advanced topics in mathematics and physics
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Optimal control of a fractional diffusion equation with state constraints
Computers & Mathematics with Applications
Optimal control of a nonhomogeneous Dirichlet boundary fractional diffusion equation
Computers & Mathematics with Applications
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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.