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Open AccessArticle

Residual Power Series Method for Fractional Swift–Hohenberg Equation

1
Department of Mathematics, Faculty of Science & Technology, Karnatak University, Dharwad 580003, India
2
Department of Mathematics and Science Education, Faculty of Education, Harran University, Sanliurfa 63100, Turkey
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Author to whom correspondence should be addressed.
Fractal Fract 2019, 3(1), 9; https://doi.org/10.3390/fractalfract3010009
Received: 20 February 2019 / Revised: 5 March 2019 / Accepted: 6 March 2019 / Published: 7 March 2019
(This article belongs to the Special Issue 2019 Selected Papers from Fractal Fract’s Editorial Board Members)
In this paper, the approximated analytical solution for the fractional Swift–Hohenberg (S–H) equation has been investigated with the help of the residual power series method (RPSM). To ensure the applicability and efficiency of the proposed technique, we consider a non-linear fractional order Swift–Hohenberg equation in the presence and absence of dispersive terms. The effect of bifurcation and dispersive parameters with physical importance on the probability density function for distinct fractional Brownian and standard motions are studied and presented through plots. The results obtained show that the proposed technique is simple to implement and very effective for analyzing the complex problems that arise in connected areas of science and technology. View Full-Text
Keywords: fractional Swift–Hohenberg equation; residual power series method; Caputo fractional derivative; Taylor series fractional Swift–Hohenberg equation; residual power series method; Caputo fractional derivative; Taylor series
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Prakasha, D.G.; Veeresha, P.; Baskonus, H.M. Residual Power Series Method for Fractional Swift–Hohenberg Equation. Fractal Fract 2019, 3, 9.

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