a semi-analytical approach for the approximate solution of casting-mould heterogeneous system

In this work, we study the variational iteration method (vim) accompanied by he’s polynomials for obtaining the solution of the temperature distribution in the casting-mould heterogeneous system with fractional order. the combined form of vim and the homotopy perturbation method (hpm) is called the variational iteration homotopy perturbation method (vihpm) which yields to implement the system of equations directly. the identification of the lagrange multiplier is essentially more reliable and higher accurate for such type of problems. the approximate solution converges rapidly to the exact solution which confirms the accuracy of this approach. some graphical representations are demonstrated to show the validity of this approach.