An efficient analytical approach for nonlinear fractional Swift-Hohenberg model involving conformable operator

The pivotal aim of the present work is to obtain analytical and approximate solution for nonlinear time-fractional Swift-Hohenberg equations (FS-HEs) using the conformable residual series method (CRSM). The fractional derivative is proposed within a conformable concept. The proposed method is graceful amalgamations of the conformable residual error functions and generalized Talyor series in the sense of conformable operator. The truncated approximate solution is substituted in the nonlinear fractional model where the conformable derivative to the residual function is equal to zero. The convergence analysis is discussed to show the accuracy and efficiency of the CRSM to obtain approximate solutions for the FS-HEs. Numerical simulation with graphical representation is also given to validate and illustrate the proposed method. The obtained results indicate that the CRS technique is effective, simple, and systematic for analyzing the behavior of nonlinear partial differential equations of fractional order arisen in many areas of physics and science.