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.

n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem.