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

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Abstract

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.

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Acknowledgements

The authors would like to thank the anonymous referees for carefully reading the manuscript and providing valuable feedback.

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  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology: VIT University, Vellore, Tamil Nadu, India

    K. Pavani & K. Raghavendar

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  1. K. Pavani
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KP: Methodology, Validation, Visualization. KR: Investigation, Methodology, Supervision, Validation, Visualization, Writing original draft.

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Correspondence to K. Raghavendar.

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Pavani, K., Raghavendar, K. Approximate Solutions of Time-Fractional Swift–Hohenberg Equation via Natural Transform Decomposition Method. Int. J. Appl. Comput. Math 9, 29 (2023). https://doi.org/10.1007/s40819-023-01493-8

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