Optimal Control of Diffusion Equation with Fractional Time Derivative with Nonlocal and Nonsingular Mittag-Leffler Kernel
Optimal Control of Diffusion Equation with Fractional Time Derivative with Nonlocal and Nonsingular Mittag-Leffler Kernel
复制标题
非局部非奇异Mittag-Leffler核分数阶时间导数扩散方程的最优控制
DOI：
10.1007/s10957-018-1305-6
复制
发表时间：
2017
影响因子：
1.9
通讯作者：
I. Area
中科院分区：
文献类型：
--
作者：
J. Djida;G. Mophou;I. Area
本文考虑Hilbert空间中具有非奇异Mittag-Leffler核的分数阶时间导数扩散方程.我们首先证明了解的存在性和唯一性的谱参数。然后，我们考虑一个分布控制分数阶扩散问题。我们证明了存在唯一的最优控制，它可以作用于系统，以便以最小的代价接近系统的状态由一个给定的状态。最后，利用Euler-Lagrange一阶最优性条件，我们得到了一个最优性系统，它刻画了最优控制。
In this paper, we consider a diffusion equation with fractional time derivative with nonsingular Mittag-Leffler kernel in Hilbert spaces. We first prove the existence and uniqueness of solution by means of a spectral argument. Then, we consider a distributed controlled fractional diffusion problem. We show that there exists a unique optimal control, which can act on the system in order to approach the state of the system by a given state at minimal cost. Finally, using the Euler–Lagrange first-order optimality condition, we obtain an optimality system, which characterizes the optimal control.