Applications of Fractional Differential Transform Method to Fractional Differential-Algebraic Equations

Abstract

In this paper, we implement fractional differential transform method (FDTM), which is a semi analytical numerical technique, to fractional differential-algebraic equations (FDAEs). The fractional derivatives are described in the Caputo sense. The method provides the solution in the form of a rapidly convergent series. The method is illustrated by four examples of FDAEs and solutions are obtained. Comparisons are made between fractional differential transform method (FDTM), Homotopy Analysis Method (HAM) and the exact solutions. The results reveal that the proposed method is very effective and simple.