Analytical solutions for time-fractional Swift-Hohenberg equations via a modified integral transform technique

Document Type : Research Paper


1 Mathematics Department, Faculty of Computer Science and Mathematics, University of Thi-Qar, Thi-Qar, Iraq

2 Department of Mathematics, Delta State University, Abraka, PMB 1, Delta State, Nigeria


In this work, the fractional natural transform decomposition method (FNTDM) is employed to obtain approximate analytical solutions for some time-fractional versions of the nonlinear Swift-Hohenberg (S-H) equation with the fractional derivatives taken in the sense of Caputo. The S-H equation models problems arising from fluid dynamics and describes temperature dynamics of thermal convection as well as complex pattern formation processes in liquid surfaces bounded along a horizontally well-conducting boundary. To explore the applicability, simplicity, and efficiency of the FNTDM, numerical simulations are provided for each of the considered problems to demonstrate the behavior of the obtained approximate solutions for different values of the fractional parameter index. The obtained simulations show a similar resemblance with those in existing related literature and further confirm the applicability of the considered method to even complex problems arising in diverse fields of applied mathematics and physics.


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Volume 13, Issue 2
July 2022
Pages 2669-2684
  • Receive Date: 11 April 2022
  • Accept Date: 05 July 2022