Conditional Stability In Determining The Zero-order Coefficient In A One Third-order Time Fractional Diffusion Equation By A Carleman Estimate

In this paper, we consider an inverse coefficient problem related to the following frac-tional diffusion equation:The inverse problem is to determine coefficient p(x) by observation data u(·,2/T) and some lateral boundary observation data.In order to solve this problem, we prove a Carleman estimate for the operator at - ax6. This Carleman estimate is hold for functions with non-compact support. This is the main difference between our Carleman estimate and the similar Carleman estimates in the lit-erature. In order to solve the inverse coefficient problem, we also prove another Carleman estimate for a fourth order operator. By relating the operator at3-ax2 to the operator at-ax6 and using the two Carleman estimates derived in this paper, we obtain the uniqueness and Holder conditional stability for the inverse coefficient problem.