Efficient Numerical Approaches for Nonlinear Fractional Partial Differential Equations Using Hybrid Decomposition

In this study, we explore the application of the hybrid decomposition method (HDM) to solve systems of fractional partial differential equations (FPDEs), which are widely encountered in various scientific disciplines. Unlike traditional numerical methods, HDM offers a non-numerical approach by decomposing the problem into manageable series solutions. This method combines the advantages of multiple decomposition techniques, providing enhanced convergence and accuracy. The hybrid decomposition method is utilized to derive solutions in the form of convergent series, demonstrating its efficiency and robustness in addressing the complexities of fractional differential equations. Our findings indicate that HDM outperforms conventional methods in terms of convergence rate and applicability to a broader range of problems. This research highlights the potential of hybrid decomposition as a powerful tool for solving fractional differential equations with greater flexibility and precision.