Determination of time dependent factors of coefficients in fractional diffusion equations

In the present paper, we consider initial-boundary value problems forpartial differential equations with time-fractional derivatives which evolvein $Q=\Omega\times(0,T)$ where $\Omega$ is a bounded domain of $\mathbb{R}^d$ and$T>0$. We study the stability of the inverse problems of determining thetime-dependent parameter in a source term or a coefficient of zero-th orderterm from observations of the solution at a point $x_0\in\overline{\Omega}$for all $t\in(0,T)$.

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