تفاصيل الرسالة العلمية

In this thesis, we obtain an approximate solution of system of fractional differential algebraic equations by using a reliable algorithm based on an adaptation of the homotopy analysis method, called the multi-step homotopy analysis method. It can be found that the corresponding numerical solutions obtained by using homotopy analysis method are valid only for a short time while the ones obtained by using the multistep homotopy analysis method are more valid and accurate during a long time. The method is only a simple modification of the homotopy analysis method, in which it is treated as an algorithm in a sequence of small intervals. The solutions obtained are also presented graphically. Comparisons between the multi-step homotopy analysis method and the exact solution reveal that this modified method is very effective and convenient