Approximate Analytical Solutions of the Time-Fractional Swift–Hohenberg Equation via Yang Transform Adomian Decomposition Method

This study examines approximate analytical solutions of the time-fractional Swift–Hohenberg equation involving the Caputo–Fabrizio fractional derivative. The main objective of this study is to investigate efficient analytical approximation techniques using the Yang transform Adomian decomposition method (YTADM). The proposed approach combines the Yang transform with the Adomian decomposition technique to construct a rapidly convergent series solution for the fractional partial differential equation. The effects of the fractional order and system parameters on the behavior of the solution have been examined via tables and are graphically represented. The results confirm that the proposed method provides accurate and computationally efficient approximate solutions to the fractional Swift–Hohenberg equation. These results show that YTADM is an appropriate and useful analytical tool to solve nonlinear fractional partial differential equations arising in mathematical physics, especially those equations involving nonsingular fractional operators. The principal contribution of this work effort is the development and application of the YTADM framework for solving the fractional Swift–Hohenberg equation; therefore, it serves as a reliable analytic tool for nonlinear fractional partial differential equations arising in mathematical physics.