Laplace transform

 

https://en.wikipedia.org/wiki/Laplace_transform

"In particular, it transforms differential equations into algebraic equations and convolution into multiplication.^[1][2][3] "

https://mathvault.ca/laplace-transform/

In fact, it takes a time-domain function, where $t$ t is the variable, and outputs a frequency-domain function, where s$s$ is the variable

It seems to me that Fourier transformation can be viewed as a special form of Laplace transformation when the alpha is zero. 

Laplace transformation is not Lapalce operator

https://en.wikipedia.org/wiki/Laplace_operator