Analytical comparisons for solving the modified fractional Kawahara equation: application on numerical simulation of chemical signaling processes

Abstract

Abstract Fractional models are essential for describing nonlinear, memory dependent wave phenomena in complex media, yet solving high order fractional nonlinear PDEs such as the Modified Caputo Fractional Kawahara Equation (MCFKE) remains challenging. This work introduces the Yang Residual Power Series Method (Yang RPSM), which integrates the Yang transform with a residual-based power series expansion to generate efficient semi-analytical solutions. Stability and convergence of the iterative scheme are established. Numerical comparisons show that the Yang RPSM outperforms natural transform decomposition technique (NTDT) and homotopy analysis technique (HAT) in accuracy and computational behavior. Applications to intracellular Ca $$^{2+}$$ propagation further demonstrate that the MCFKE effectively captures memory effects, nonlinear wave steepening, and dispersion-driven attenuation. The Yang RPSM provides a reliable computational tool for high order fractional PDEs and highlights the MCFKE as a biologically meaningful model for anomalous, memory driven wave processes.