I am wondering how to prove the below Fourier transform is non-negative? I did much simulation and it seems to be non-negative. Thanks!

$$\int_0^\inf (be^{-at^p}-ae^{-bt^p})cos(tx)dt, 0<a<b, \frac{1}{2}<p<1$$

I am wondering how to prove the below Fourier transform is non-negative? I did much simulation and it seems to be non-negative.

$$\int_0^\inf (be^{-at^p}-ae^{-bt^p})\cos(tx)dt, 0<a<b, \frac{1}{2}<p<1$$