Analytical treatment of fractional Swift-Hohenberg equation with uncertainty

Abstract

In this article, we present the time-fractional Swift-Hohenberg equation (FSFE) with uncertainty where the fractional deriative is chossen in caputo sense. We have solved the fuzzy FSFE by homotopy analysis elzaki transform method (HAETM) which is a collaboration of homotopy analysis method with elzaki transform.The proposed algorithm provides a fast convergence series solution. Three dimensional plots of the solutions, error graphs and h-cut graphs are given to illustrate the efficacy of the method to solve FSFE.

Keywords

• fractional swift-hohenberg equation
• homotopy analysis elzaki transform method
• uncertain environment
• upper and lower bound approximate solutions