A comparison study of two modified analytical approach for the solution of nonlinear fractional shallow water equations in fluid flow

In this study, a comparison between the modified homotopy analysis transform method (MHATM) and residual power series method (RPSM) have been given for solving time-fractional coupled shallow water equations (SWEs). The time-fractional coupled SWEs are a system of PDEs that describe the flow below a pressure surface in a fluid is considered. Rigorous convergence analysis and error estimated have been exhibited for both the featured methods. The results obtained by MHATM and RPSM are then compared with well-known exact solutions. To show the effectiveness and advantage of the featured techniques the numerical simulation of coupled SWEs has been represented graphically with tabulated data. However, the results indicate that MHATM provides more accurate value than RPSM for solving fractional coupled SWEs.