Fractional View Analysis of Swift–Hohenberg Equations by an Analytical Method and Some Physical Applications

Abstract

This study investigates the fractional-order Swift–Hohenberg equations using the natural decomposition method with non-singular kernel derivatives. The fractional derivative in the sense of Caputo–Fabrizio is considered. The Adomian decomposition technique (ADT) is a great deal to the overall natural transformation to create closed-form results of the given models. This technique provides a closed-form result for the suggested models. In addition, this technique is attractive, simple, and preferred over other techniques. The graphs of the solution in fractional and integer-order show that the achieved solutions are very close to the actual result of the examples. It is also investigated that the result of fractional-order models converges to the integer-order model’s solution. Furthermore, the proposed method validity is examined using numerical examples. The obtained results for the given problems fully support the theory of the proposed method. The present method is a straightforward and accurate analytical method to analyze other fractional-order partial differential equations, such as many evolution equations that govern the dynamics of nonlinear waves in plasma physics.