تفاصيل الرسالة العلمية

In this thesis, based on the homotopy analysis method, a new analytic technique is proposed to solve system of fractional integral differential equations. A new reliable algorithm called the Laplace homotopy analysis method. The proposed algorithm presents a procedure of constructing the set of base functions and gives the high-order deformation equation in a simple form. The method provides the solution in the form of a rapidly convergent series. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method. Comparisons between the Laplace homotopy analysis method and the exact solution in the case of intger-order derivatives reveal that the new technique is a promising tool for nonlinear problems of integer and fractional order