Based on Electromagnetic thermoelastic constitutive equations,its increased dimensions constitutive relationship on the basis of relevant literature was established,and the electromagnetic thermo-elastic material generic shell homogeneous state equations were derived. Then,by Laplace transform onthe homogeneous state equation,complex high-order terms form of the polynomial coefficient matrix can be got. Considering the convenience and efficiency to solve the problem of inverse transform,the article made a fractional separation process on complex high-order coefficient matrix after Laplace transform which had complex high-order polynomial terms. Finally,numerical examples show that the method is correctness,and the computational efficiencyis almost the same as the precise integration method.