“gcdAlpha” – a semi-analytical method for solving fractional state equations

The paper discusses a semi-analytical method for solving systems of fractional state equations with various orders. The method bases on an expansion of the system into one where there is a single derivative order. The formulation of the matrices of the new system is explained in detail. Another characteristic feature of the method is also introduced – a consideration of forms, in which the time functions appear and the terms appearing in the solution as a result. A fractional circuit example is presented in order to test the method. The computation time for the method is also studied.