On an extension of the Mikusinski type operational calculus for the Caputo fractional derivative

In this paper, a two-parameter extension of the operational calculus of Mikusinski's type for the Caputo fractional derivative is presented. The first parameter is connected with the rings of functions that are used as a basis for construction of the convolution quotients fields. The convolutions by themselves are characterized by another parameter. The obtained two-parameter operational calculi are compared each to other and some homomorphisms between the fields of convolution quotients are established.