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arXiv · 1711.09070

Optimal control of diffusion equation with fractional time derivative with nonlocal and nonsingular Mittag-Leffler kernel

J. D. Djida·G. M. Mophou·I. Area
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Abstract

In this paper, we consider a diffusion equation with fractional-time derivative with nonsingular Mittag-Leffler kernel in Hilbert spaces. Existence and uniqueness of solution are proved by means of a spectral argument. The existence of solution is obtained for all values of the fractional parameter $\alpha \in (0,1)$. Moreover, by applying control theory to the fractional diffusion problem we obtain an optimality system which has also a unique solution.

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J. D. Djida, G. M. Mophou, I. Area. 2017-11-24. Optimal control of diffusion equation with fractional time derivative with nonlocal and nonsingular Mittag-Leffler kernel. https://arxiv.org/abs/1711.09070

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