Generalized Variational Iteration Method for Solve Fractional Differential Equations

Abstract

In recent years, numerical techniques for solving fractional differential equations (FDEs) have gained significant attention due to their applications in various fields. One method that has shown promise is the Variational Iteration Method (VIM). However, challenges remain in addressing boundary value problems (BVPs) with high accuracy. To address this gap, this study introduces the Generalized Variational Iteration Method (GVIM), an extension of VIM specifically designed for BVPs. The proposed method delivers highly accurate solutions with evenly distributed errors across the domain. Numerical results demonstrate the method's superior convergence and reliability compared to existing techniques, offering a robust tool for solving complex FDEs in scientific and engineering applications.