Numerical Solution of Composite Fractional Oscillation Equation by Fractional Differential Transform Method and Variational Iteration Method

This research aims to find the numerical solution of nonlinear composite fractional oscillation equation using Fractional Differential Transform Method (FDTM) and Variational Iteration Method (VIM). The numerical solutions demonstrate that the two approaches agree fairly well. As a result, these two approaches represent extremely strong and effective methods for resolving various types of fractional differential equations, both linear and non-linear, that arise in numerous technological and engineering domains. We can conclude that both approaches are highly effective and potent in obtaining both numerical and analytical resolutions for a broad range of FDEs. However, the FDTM solves nonlinear problem more closer to the exact solution, giving it an advantage over the VIM.