A hybrid analytical method for fractional order Klein–Gordon and Burgers equations

In this study, fractional-order partial differential equations (FPDEs), specifically the Klein–Gordon equation (KGE) and the Burgers equation, are analytically solved using a modified and combined version of the Elzaki Decomposition Technique (ETADM). To assess the efficacy and robustness of the proposed approach, several examples are provided to obtain analytical and numerical results related to the KGE and the Burgers equation. Furthermore, the proposed techniques yield convergent series solutions with well-defined components, without the need for perturbation or linearization. Additionally, we compare several methods for solving differential equations arising in physics and engineering, including ETADM, the Variational Iteration Method (VIM), and the Adomian Decomposition Method (ADM). For comparison and validation, three examples are presented, along with the results obtained using both ETADM and VIM.