Analysis of fractional Swift-Hohenberg models using highly accurate techniques within the Caputo operator framework

This investigation aims to analyze and solve the fractional SwiftHohenberg (FSH) equation using the Aboodh residual power series method (ARPSM) and Aboodh transform iterative method (ATIM) within the Caputo operator framework. This equation is widely used in modeling pattern formation phenomena in various physical systems. Thus, the current study focuses on understanding the mechanics and dynamics of wave propagation described by this equation. Additionally, it investigates the impact of the fractional parameter on the behavior of these waves. By employing both ARPSM and ATIM, we aim to obtain highly accurate and efficient approximations to this equation. The effectiveness of these methods is demonstrated through numerical simulations, where we compare the obtained results with existing analytical and numerical solutions. Our findings highlight the utility of the ARPSM and ATIM in studying complex nonlinear fractional differential equations, providing valuable insights into pattern formation dynamics governed by the Swift-Hohenberg equation.