Residual Power Series Method for Fractional Swift–Hohenberg Equation

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 fra...
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Autor*in:	D. G. Prakasha [verfasserIn] P. Veeresha [verfasserIn] Haci Mehmet Baskonus [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	fractional Swift–Hohenberg equation residual power series method Caputo fractional derivative Taylor series

Übergeordnetes Werk:	In: Fractal and Fractional - MDPI AG, 2018, 3(2019), 1, p 9
Übergeordnetes Werk:	volume:3 ; year:2019 ; number:1, p 9

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/fractalfract3010009

Katalog-ID:	DOAJ073322261

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520			\|a 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.
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allfields	10.3390/fractalfract3010009 doi (DE-627)DOAJ073322261 (DE-599)DOAJ016924e1a85a4b40bc6a2230b25f574f DE-627 ger DE-627 rakwb eng QC310.15-319 QA1-939 QA299.6-433 D. G. Prakasha verfasserin aut Residual Power Series Method for Fractional Swift–Hohenberg Equation 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. fractional Swift–Hohenberg equation residual power series method Caputo fractional derivative Taylor series Thermodynamics Mathematics Analysis P. Veeresha verfasserin aut Haci Mehmet Baskonus verfasserin aut In Fractal and Fractional MDPI AG, 2018 3(2019), 1, p 9 (DE-627)897435656 (DE-600)2905371-7 25043110 nnns volume:3 year:2019 number:1, p 9 https://doi.org/10.3390/fractalfract3010009 kostenfrei https://doaj.org/article/016924e1a85a4b40bc6a2230b25f574f kostenfrei http://www.mdpi.com/2504-3110/3/1/9 kostenfrei https://doaj.org/toc/2504-3110 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2019 1, p 9
spelling	10.3390/fractalfract3010009 doi (DE-627)DOAJ073322261 (DE-599)DOAJ016924e1a85a4b40bc6a2230b25f574f DE-627 ger DE-627 rakwb eng QC310.15-319 QA1-939 QA299.6-433 D. G. Prakasha verfasserin aut Residual Power Series Method for Fractional Swift–Hohenberg Equation 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. fractional Swift–Hohenberg equation residual power series method Caputo fractional derivative Taylor series Thermodynamics Mathematics Analysis P. Veeresha verfasserin aut Haci Mehmet Baskonus verfasserin aut In Fractal and Fractional MDPI AG, 2018 3(2019), 1, p 9 (DE-627)897435656 (DE-600)2905371-7 25043110 nnns volume:3 year:2019 number:1, p 9 https://doi.org/10.3390/fractalfract3010009 kostenfrei https://doaj.org/article/016924e1a85a4b40bc6a2230b25f574f kostenfrei http://www.mdpi.com/2504-3110/3/1/9 kostenfrei https://doaj.org/toc/2504-3110 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2019 1, p 9
allfields_unstemmed	10.3390/fractalfract3010009 doi (DE-627)DOAJ073322261 (DE-599)DOAJ016924e1a85a4b40bc6a2230b25f574f DE-627 ger DE-627 rakwb eng QC310.15-319 QA1-939 QA299.6-433 D. G. Prakasha verfasserin aut Residual Power Series Method for Fractional Swift–Hohenberg Equation 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. fractional Swift–Hohenberg equation residual power series method Caputo fractional derivative Taylor series Thermodynamics Mathematics Analysis P. Veeresha verfasserin aut Haci Mehmet Baskonus verfasserin aut In Fractal and Fractional MDPI AG, 2018 3(2019), 1, p 9 (DE-627)897435656 (DE-600)2905371-7 25043110 nnns volume:3 year:2019 number:1, p 9 https://doi.org/10.3390/fractalfract3010009 kostenfrei https://doaj.org/article/016924e1a85a4b40bc6a2230b25f574f kostenfrei http://www.mdpi.com/2504-3110/3/1/9 kostenfrei https://doaj.org/toc/2504-3110 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2019 1, p 9
allfieldsGer	10.3390/fractalfract3010009 doi (DE-627)DOAJ073322261 (DE-599)DOAJ016924e1a85a4b40bc6a2230b25f574f DE-627 ger DE-627 rakwb eng QC310.15-319 QA1-939 QA299.6-433 D. G. Prakasha verfasserin aut Residual Power Series Method for Fractional Swift–Hohenberg Equation 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. fractional Swift–Hohenberg equation residual power series method Caputo fractional derivative Taylor series Thermodynamics Mathematics Analysis P. Veeresha verfasserin aut Haci Mehmet Baskonus verfasserin aut In Fractal and Fractional MDPI AG, 2018 3(2019), 1, p 9 (DE-627)897435656 (DE-600)2905371-7 25043110 nnns volume:3 year:2019 number:1, p 9 https://doi.org/10.3390/fractalfract3010009 kostenfrei https://doaj.org/article/016924e1a85a4b40bc6a2230b25f574f kostenfrei http://www.mdpi.com/2504-3110/3/1/9 kostenfrei https://doaj.org/toc/2504-3110 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2019 1, p 9
allfieldsSound	10.3390/fractalfract3010009 doi (DE-627)DOAJ073322261 (DE-599)DOAJ016924e1a85a4b40bc6a2230b25f574f DE-627 ger DE-627 rakwb eng QC310.15-319 QA1-939 QA299.6-433 D. G. Prakasha verfasserin aut Residual Power Series Method for Fractional Swift–Hohenberg Equation 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. fractional Swift–Hohenberg equation residual power series method Caputo fractional derivative Taylor series Thermodynamics Mathematics Analysis P. Veeresha verfasserin aut Haci Mehmet Baskonus verfasserin aut In Fractal and Fractional MDPI AG, 2018 3(2019), 1, p 9 (DE-627)897435656 (DE-600)2905371-7 25043110 nnns volume:3 year:2019 number:1, p 9 https://doi.org/10.3390/fractalfract3010009 kostenfrei https://doaj.org/article/016924e1a85a4b40bc6a2230b25f574f kostenfrei http://www.mdpi.com/2504-3110/3/1/9 kostenfrei https://doaj.org/toc/2504-3110 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 3 2019 1, p 9
language	English
source	In Fractal and Fractional 3(2019), 1, p 9 volume:3 year:2019 number:1, p 9
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topic_facet	fractional Swift–Hohenberg equation residual power series method Caputo fractional derivative Taylor series Thermodynamics Mathematics Analysis
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container_title	Fractal and Fractional
authorswithroles_txt_mv	D. G. Prakasha @@aut@@ P. Veeresha @@aut@@ Haci Mehmet Baskonus @@aut@@
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callnumber-first	Q - Science
author	D. G. Prakasha
spellingShingle	D. G. Prakasha misc QC310.15-319 misc QA1-939 misc QA299.6-433 misc fractional Swift–Hohenberg equation misc residual power series method misc Caputo fractional derivative misc Taylor series misc Thermodynamics misc Mathematics misc Analysis Residual Power Series Method for Fractional Swift–Hohenberg Equation
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topic_title	QC310.15-319 QA1-939 QA299.6-433 Residual Power Series Method for Fractional Swift–Hohenberg Equation fractional Swift–Hohenberg equation residual power series method Caputo fractional derivative Taylor series
topic	misc QC310.15-319 misc QA1-939 misc QA299.6-433 misc fractional Swift–Hohenberg equation misc residual power series method misc Caputo fractional derivative misc Taylor series misc Thermodynamics misc Mathematics misc Analysis
topic_unstemmed	misc QC310.15-319 misc QA1-939 misc QA299.6-433 misc fractional Swift–Hohenberg equation misc residual power series method misc Caputo fractional derivative misc Taylor series misc Thermodynamics misc Mathematics misc Analysis
topic_browse	misc QC310.15-319 misc QA1-939 misc QA299.6-433 misc fractional Swift–Hohenberg equation misc residual power series method misc Caputo fractional derivative misc Taylor series misc Thermodynamics misc Mathematics misc Analysis
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title	Residual Power Series Method for Fractional Swift–Hohenberg Equation
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title_full	Residual Power Series Method for Fractional Swift–Hohenberg Equation
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title_sort	residual power series method for fractional swift–hohenberg equation
callnumber	QC310.15-319
title_auth	Residual Power Series Method for Fractional Swift–Hohenberg Equation
abstract	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.
abstractGer	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.
abstract_unstemmed	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.
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title_short	Residual Power Series Method for Fractional Swift–Hohenberg Equation
url	https://doi.org/10.3390/fractalfract3010009 https://doaj.org/article/016924e1a85a4b40bc6a2230b25f574f http://www.mdpi.com/2504-3110/3/1/9 https://doaj.org/toc/2504-3110
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Residual Power Series Method for Fractional Swift–Hohenberg Equation

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