  In this paper, we introduce a Matlab program method to compute Carleman
estimate for the fourth order partial differential operator
$\gamma\partial_t+\partial_x^4\ (\gamma\in\mathbb{R})$. We obtain two kinds of
Carleman estimates with different weight functions, i.e. singular weight
function and regular weight function, respectively. Based on Carleman estimate
with singular weight function, one can obtain the known controllability and
observability results for the 1-d fourth order parabolic-type equation, while
based on Carleman estimate with regular weight function, one can deduce not
only the known result on conditional stability in the inverse problem of
half-order fractional diffusion equation, but also a new result on conditional
stability in the inverse problem of half-order fractional Schr\"odinger
equation.
