Performance Comparison of Techniques for Fractional Kawahara and Modified Kawahara Equations in Blood Flow Dynamics

The Kawahara equation and its modified form are nonlinear dispersive partial differential equations commonly used to model wave propagation in fluids and plasmas. In hemodynamic studies, these equations have been adapted to describe the propagation of pulse waves in large arteries, where dispersive wave effects play an important role in capturing the dynamics of blood flow. In this study, we focus on their time fractional generalizations within the Caputo sense and construct approximate analytical solutions by employing the optimal auxiliary function method (OAFM). This technique generates auxiliary functions with adjustable parameters, which enhances both accuracy and convergence speed. By applying OAFM to the time fractional Caputo Kawahara (TCFKE) and modified Kawahara (MTCFKE) equations, we obtain symmetric approximate solutions and confirm their efficiency through numerical tests and graphical illustrations. Moreover, in the context of fluid flow and shallow water wave propagation, comparative analysis with other existing methods including the homotopy analysis method, residual power series method, and natural transform decomposition technique highlights the robustness and higher accuracy of OAFM.