A new application of Khalouta differential transform method and convergence analysis to solve nonlinear fractional Liénard equation

In this study, we propose a new hybrid numerical method called the Khalouta differential transform method to solve the nonlinear fractional Liénard equation involving the Caputo fractional derivative. The convergence theorem of the proposed method is proved under suitable conditions.
The Khalouta differential transform method is a semi-analytical technique that combines two powerful methods: the Khalouta transform method and the differential transform method. The main advantage of this approach is that it provides very fast solutions without requiring linearization, perturbation, or any other assumptions. The proposed method is described and illustrated with two numerical examples. The illustrative examples show that the numerical results obtained are in very good agreement with the exact solutions. This confirms the accuracy and effectiveness of the proposed method.