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February  2020, 25(2): 761-779. doi: 10.3934/dcdsb.2019266

## On an optimal control problem of time-fractional advection-diffusion equation

 China university of Geosciences, Wuhan, Hubei province, China

* Corresponding author: Qing Tang

Received  January 2019 Revised  April 2019 Published  November 2019

We consider an optimal control problem of an advection-diffusion equation with Caputo time-fractional derivative. By convex duality method we obtain as optimality condition a forward-backward coupled system. We then prove the existence of a solution to this coupled system using Schauder fixed point theorem. The uniqueness of the solution is also established under certain monotonicity condition on the cost functional.

Citation: Qing Tang. On an optimal control problem of time-fractional advection-diffusion equation. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 761-779. doi: 10.3934/dcdsb.2019266
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