Approximate Solutions of Time-Fractional Swift–Hohenberg Equation via Natural Transform Decomposition Method

• Published in: International journal of applied and computational mathematics Vol. 9; no. 3
• Main Authors: Pavani, K., Raghavendar, K.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01-06-2023; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied mathematics; Computational mathematics; Computational Science and Engineering; Decomposition; Differential equations; Effectiveness; Fractional calculus; Kernels; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Theoretical; Natural transform decomposition; Caputo–Fabrizio derivative; Atangana–Baleanu–Caputo derivative; Swift–Hohenberg equation; Caputo derivative
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-023-01493-8

In this study, we apply the natural transform decomposition approach to analyse the time-fractional Swift–Hohenberg problem. The Caputo derivative, a well-known singular kernel derivative, is discussed along with the Caputo–Fabrizio and Atangana–Baleanu derivative in Caputo sense, which are non-singular kernel derivatives. To get the solution, we used the natural transform followed by inverse natural transform. Convergence and uniqueness of the solutions presented. The numerical simulations are offered to guarantee the effectiveness of the method under investigation. The current approach clearly demonstrates how the results for various fractional orders behave. The findings of this study demonstrate the effectiveness and dependability of the suggested method for the analysis of fractional differential equations. The acquired results are compared to the existing solutions numerically and graphically. The results demonstrate the effectiveness, potency, and dependability of the current technique. A variety of partial fractional differential equations can be solved using the presented method.