In this note a singular abstract Cauchy problem is considered. A solution is obtained for this problem in terms of a regular abstract Cauchy problem. As an application we obtain a new solution of the initial value problem for a class of singular partial differential equations.

The goal of this work is to introduce the two-parameter conformable fractional semigroups and provide a definition its infinitesimal generator. For such generators, we develop multiple results. In addition, show that solution for abstract Cauchy problems.