H. M. Jaradat, M. Zurigat, Safwan Al-shara and Qutaibeh Katatbeh, Toward a new algorithm for systems of fractional algebraic-differential equations, Italian Journal of Pure and Applied Mathematics, 32 (2014), 579-594.

This paper is concerned with the development of an e? cient algorithm for the analytic solutions of systems of fractional di¤erential -algebraic equations (FDAE). The proposed algorithm is an elegant combination of the Laplace transform method (LTM) with the homotopy analysis method (HAM). The biggest advantage of the Laplace homotopy analysis method (LHAM) over the existing standard analyti- cal techniques is that it overcomes the di? culty arising in calculating complicated terms. Numerical examples are examined to highlight the signi…cant features of this method.