Improving homotopy analytical method with sine cosine algorithm and Simpson integrative method for solving fractional ordinary differential equations.

In this paper, we will solve ordinary differential equations of fractional order by homotopy analytical method (HAM), We will also improve HAM by using the sine cosine algorithm with Simpson's 3/8 integral rule, where the SCA using to adjusts and modifies the parameter ℎ and picks its best value, then Simpson's 3/8 integral rule will solve the final series of (HAM-SCA) to obtain a best approximate solution than the previous methods. The proposed method (HAM-SCA-SIMP) yields a solution characterized by reliability and efficiency corresponding to HAM and the HAM-SCA hybrid method by calculating the maximum absolute error MAE and the mean square error MSE. [ABSTRACT FROM AUTHOR]