A Novel Numeric-analytic Method for Time-fractional Swift–Hohenberg (S–H) Equation with Modified Caputo-Fabrizio Derivative

This work investigates utilizing Adomian decomposition technique (A-ADM) coupled with Aboodh transform as a hybrid approach the solution of Caputo-Fabrizio (CF) fractional order Swift-Hohenberg problem. Effective framework for modeling memory effects and complex system dynamics is provided by CF fractional derivative defined by non-singular exponential kernel. Classical Swift-Hohenberg equation is expanded to account for long-term memory effects, which are crucial in understanding pattern development and chaotic behavior in many physical systems by including CF fractional derivatives. With the suggested Aboodh-Adomian decomposition technique (A-ADM), an approximate analytical solution is provided showing its efficiency and accuracy in solving fractional nonlinear problem. Furthermore shown are convergence and originality of the solution. Graphical depictions of the acquired solutions make use of MATLAB package software. Theoretical results are confirmed by numerical simulations, which further expose the important influence of fractional order on the dynamic features of the system.