Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems

In this investigation, the fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) problem is solved using two modern semi-analytic techniques known as the Aboodh residual power series method (ARPSM) and Aboodh transform iteration method (ATIM). The two suggested approaches are briefly explained, along with how to use them to solve the fractional Hirota–Satsuma coupled KdV problem. Some analytical approximate solutions for the current problem are derived using the proposed techniques until the second-order approximation. To ensure high accuracy of the derived approximation, they are analyzed numerically and graphically and compared with the exact solutions of the integer cases. The offered techniques demonstrate more accuracy in their outcomes compared to other alternatives. The numerical results show that ARPSM and ATIM are highly accurate, practical, and beneficial for solving nonlinear equation systems. The current results are expected to help many physics researchers in modeling their different physical problems, especially those interested in plasma physics.