Conformable Fractional Reduced Differential Transform Method for Solving Linear and Nonlinear Time-Fractional Swift-Hohenberg (S-H) Equation

S.S. Omorodion¹

Section:Research Paper, Product Type: Journal-Paper
Vol.8 , Issue.6 , pp.20-29, Dec-2021

Online published on Dec 31, 2021

Copyright © S.S. Omorodion . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we present the conformable fractional reduced differential transform method (CFRDTM) for finding the exact and approximate analytical solution for the time-fractional Swift-Hohenberg (S-H) equations with initial value. The S-H equation was first proposed in 1977 by J.B. Swift and P.C. Hohenberg to study the thermal fluctuations on a fluid near the Rayleigh-Benard convective instability. To demonstrate the efficiency and applicability of the proposed method, we considered linear and nonlinear time-fractional S-H equations with and without dispersive terms. Results are calculated and presented through 2D/3D graphical representations. The obtained results show that the CFRDTM is effective and simple in constructing the exact and approximate analytical solutions for the time fractional S-H equations, and it may also find wide application in other complicated fractional partial differential equations that originate in the areas of engineering and science.

Key-Words / Index Term :
Conformable Derivative, Conformable Fractional Reduced Differential Transform Method, Fractional Calculus, Time-Fractional Swift-Hohenberg Equation

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