  This article is devoted to the noncommutative version of the Laplace
transformation. New types of the direct and inverse transformations of the
Laplace type over general Cayley-Dickson algebras, in particular, also the skew
field of quaternions and the octonion algebra are investigated. Examples are
given. Theorems are proved about properties of such transformations and also
theorems about images and originals in conjunction with operations of
multiplication, differentiation, integration, convolution, shift and homothety.
The noncommutative analog of the Mellin transformation is studied as well.
Applications are given to solutions of differential equations over the
Cayley-Dickson algebras.
