ANALYSIS OF THE CONFORMABLE TEMPORAL-FRACTIONAL SWIFT-HOHENBERG EQUATION USING A NOVEL COMPUTATIONAL TECHNIQUE

The main objective of this study is to provide a new computational procedure for extracting approximate and exact solutions of the temporal-fractional Swift-Hohenberg (S-H) equations in the context of conformable derivatives using the conformable natural transform (CNT) and Daftardar-Jafari method (DJM). We refer to it as the natural conformable Daftardar-Jafari method (CNDJM). The three types of errors are assessed in order to gauge the efficiency and consistency of the proposed method. Furthermore, 2D and 3D graphics are used to compare the exact and approximate solutions. This method offers a considerable benefit over homotopy analysis and Adomian decomposition methods in terms of computational work because it does not require Adomian and He's polynomials. The procedure is quick and easy to use.

Automated summary

The aim of this study is to introduce a new computational method, the natural conformable Daftardar-Jafari method (CNDJM), for extracting approximate and exact solutions of the temporal-fractional Swift-Hohenberg (S-H) equations using the conformable natural transform (CNT) and Daftardar-Jafari method (DJM). The efficiency and consistency of the proposed method are assessed by evaluating three types of errors. 2D and 3D graphics are utilized to compare the exact and approximate solutions. This method offers advantages over homotopy analysis and Adomian decomposition methods as it does not require Adomian and He's polynomials, significantly reducing computational work.