CHAOTIC BEHAVIOR IN FRACTIONAL HELMHOLTZ AND KELVIN–HELMHOLTZ INSTABILITY PROBLEMS WITH RIESZ OPERATOR
This paper introduces some important dissipative problems that are recent and still of intermittent interest. The classical dynamics of Helmholtz and Kelvin–Helmholtz instability equations are modeled with the Riesz operator which incorporates the left- and right-sided of the Riemann–Liouville non-i...
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| Veröffentlicht in: | Fractals (Singapore) 2022-08, Vol.30 (5) |
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| creator | OWOLABI, KOLADE M. GÓMEZ-AGUILAR, J. F. KARACA, YELIZ LI, YONG-MIN SALEH, BAHAA ALY, AYMAN A. |
| description | This paper introduces some important dissipative problems that are recent and still of intermittent interest. The classical dynamics of Helmholtz and Kelvin–Helmholtz instability equations are modeled with the Riesz operator which incorporates the left- and right-sided of the Riemann–Liouville non-integer order operators to mimic naturally the physical patterns of these models arising in hydrodynamics and geophysical fluids. The Laplace and Fourier transform techniques are used to approximate the Riesz fractional operator in a spatial direction. The behaviors of the Helmholtz and Kelvin–Helmholtz equations are observed for some values of fractional power in the regimes,
0
<
α
≤
1
and
1
<
α
≤
2
, using different boundary conditions on a square domain in 1D, 2D and 3D (spatial-dimensions). Numerical results reveal some astonishing and very impressive phenomena which arise due to the variations in the initial and source function, as well as fractional parameter
α
, for subdiffusive and superdiffusive scenarios. |
| doi_str_mv | 10.1142/S0218348X2240182X |
| format | Article |
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0
<
α
≤
1
and
1
<
α
≤
2
, using different boundary conditions on a square domain in 1D, 2D and 3D (spatial-dimensions). Numerical results reveal some astonishing and very impressive phenomena which arise due to the variations in the initial and source function, as well as fractional parameter
α
, for subdiffusive and superdiffusive scenarios.</description><identifier>ISSN: 0218-348X</identifier><identifier>EISSN: 1793-6543</identifier><identifier>DOI: 10.1142/S0218348X2240182X</identifier><language>eng</language><publisher>Singapore: World Scientific Publishing Company</publisher><subject>Boundary conditions ; Dynamic stability ; Fourier transforms ; Geophysical fluids ; Helmholtz equations ; Kelvin-Helmholtz instability ; Mathematical models ; Operators (mathematics)</subject><ispartof>Fractals (Singapore), 2022-08, Vol.30 (5)</ispartof><rights>2022, The Author(s)</rights><rights>2022. The Author(s). This is an Open Access article in the “Special Issue Section on Fractal AI-Based Analyses and Applications to Complex Systems: Part III”, edited by Yeliz Karaca (University of Massachusetts Medical School, USA), Dumitru Baleanu (Cankaya University, Turkey), Majaz Moonis (University of Massachusetts Medical School, USA), Yu-Dong Zhang (University of Leicester, UK) & Osvaldo Gervasi (Perugia University, Italy) published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 (CC-BY-NC-ND) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c357X-7c4e5e3d41ecaa8573b79db1e27a42db409bd20839b125abf173aa5b286db52f3</citedby><cites>FETCH-LOGICAL-c357X-7c4e5e3d41ecaa8573b79db1e27a42db409bd20839b125abf173aa5b286db52f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.worldscientific.com/doi/reader/10.1142/S0218348X2240182X$$EPDF$$P50$$Gworldscientific$$Hfree_for_read</linktopdf><link.rule.ids>314,776,780,27476,27903,27904,55547</link.rule.ids><linktorsrc>$$Uhttp://dx.doi.org/10.1142/S0218348X2240182X$$EView_record_in_World_Scientific_Publishing$$FView_record_in_$$GWorld_Scientific_Publishing$$Hfree_for_read</linktorsrc></links><search><creatorcontrib>OWOLABI, KOLADE M.</creatorcontrib><creatorcontrib>GÓMEZ-AGUILAR, J. F.</creatorcontrib><creatorcontrib>KARACA, YELIZ</creatorcontrib><creatorcontrib>LI, YONG-MIN</creatorcontrib><creatorcontrib>SALEH, BAHAA</creatorcontrib><creatorcontrib>ALY, AYMAN A.</creatorcontrib><title>CHAOTIC BEHAVIOR IN FRACTIONAL HELMHOLTZ AND KELVIN–HELMHOLTZ INSTABILITY PROBLEMS WITH RIESZ OPERATOR</title><title>Fractals (Singapore)</title><description>This paper introduces some important dissipative problems that are recent and still of intermittent interest. The classical dynamics of Helmholtz and Kelvin–Helmholtz instability equations are modeled with the Riesz operator which incorporates the left- and right-sided of the Riemann–Liouville non-integer order operators to mimic naturally the physical patterns of these models arising in hydrodynamics and geophysical fluids. The Laplace and Fourier transform techniques are used to approximate the Riesz fractional operator in a spatial direction. The behaviors of the Helmholtz and Kelvin–Helmholtz equations are observed for some values of fractional power in the regimes,
0
<
α
≤
1
and
1
<
α
≤
2
, using different boundary conditions on a square domain in 1D, 2D and 3D (spatial-dimensions). Numerical results reveal some astonishing and very impressive phenomena which arise due to the variations in the initial and source function, as well as fractional parameter
α
, for subdiffusive and superdiffusive scenarios.</description><subject>Boundary conditions</subject><subject>Dynamic stability</subject><subject>Fourier transforms</subject><subject>Geophysical fluids</subject><subject>Helmholtz equations</subject><subject>Kelvin-Helmholtz instability</subject><subject>Mathematical models</subject><subject>Operators (mathematics)</subject><issn>0218-348X</issn><issn>1793-6543</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>ADCHV</sourceid><recordid>eNplkMtKw0AYhQdRsFYfwN2A6-hcO8lyGlMzOE1KEmvtJmRywZRqatIi7nwH39AnsaWii64O_Od8_4EDwCVG1xgzchMjgm3K7BkhDGGbzI5ADwuHWgPO6DHo7Wxr55-Cs65bIIQYw6wHnl1fholy4dDz5VSFEVQBHEXSTVQYSA19T4_9UCdzKINbeO_pqQq-P7_-zyqIEzlUWiVPcBKFQ-2NY_ioEh9GyovnMJx4kUzC6BycVNmyKy9-tQ8eRl7i-pYO75QrtZVTLmaWyFnJS1owXOZZZnNBjXAKg0siMkYKw5BjCoJs6hhMeGYqLGiWcUPsQWE4qWgfXO3_rtrmbVN263TRbNrXbWVKBBKYUMb5NoX3qbxtuq4tq3TV1i9Z-5FilO4GTQ8G3TJoz7w37bLo8rp8XddVnf-hh8gPcfhxBw</recordid><startdate>202208</startdate><enddate>202208</enddate><creator>OWOLABI, KOLADE M.</creator><creator>GÓMEZ-AGUILAR, J. F.</creator><creator>KARACA, YELIZ</creator><creator>LI, YONG-MIN</creator><creator>SALEH, BAHAA</creator><creator>ALY, AYMAN A.</creator><general>World Scientific Publishing Company</general><general>World Scientific Publishing Co. Pte., Ltd</general><scope>ADCHV</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>202208</creationdate><title>CHAOTIC BEHAVIOR IN FRACTIONAL HELMHOLTZ AND KELVIN–HELMHOLTZ INSTABILITY PROBLEMS WITH RIESZ OPERATOR</title><author>OWOLABI, KOLADE M. ; GÓMEZ-AGUILAR, J. F. ; KARACA, YELIZ ; LI, YONG-MIN ; SALEH, BAHAA ; ALY, AYMAN A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c357X-7c4e5e3d41ecaa8573b79db1e27a42db409bd20839b125abf173aa5b286db52f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Boundary conditions</topic><topic>Dynamic stability</topic><topic>Fourier transforms</topic><topic>Geophysical fluids</topic><topic>Helmholtz equations</topic><topic>Kelvin-Helmholtz instability</topic><topic>Mathematical models</topic><topic>Operators (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>OWOLABI, KOLADE M.</creatorcontrib><creatorcontrib>GÓMEZ-AGUILAR, J. F.</creatorcontrib><creatorcontrib>KARACA, YELIZ</creatorcontrib><creatorcontrib>LI, YONG-MIN</creatorcontrib><creatorcontrib>SALEH, BAHAA</creatorcontrib><creatorcontrib>ALY, AYMAN A.</creatorcontrib><collection>World Scientific Open</collection><collection>CrossRef</collection><jtitle>Fractals (Singapore)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>OWOLABI, KOLADE M.</au><au>GÓMEZ-AGUILAR, J. F.</au><au>KARACA, YELIZ</au><au>LI, YONG-MIN</au><au>SALEH, BAHAA</au><au>ALY, AYMAN A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>CHAOTIC BEHAVIOR IN FRACTIONAL HELMHOLTZ AND KELVIN–HELMHOLTZ INSTABILITY PROBLEMS WITH RIESZ OPERATOR</atitle><jtitle>Fractals (Singapore)</jtitle><date>2022-08</date><risdate>2022</risdate><volume>30</volume><issue>5</issue><issn>0218-348X</issn><eissn>1793-6543</eissn><abstract>This paper introduces some important dissipative problems that are recent and still of intermittent interest. The classical dynamics of Helmholtz and Kelvin–Helmholtz instability equations are modeled with the Riesz operator which incorporates the left- and right-sided of the Riemann–Liouville non-integer order operators to mimic naturally the physical patterns of these models arising in hydrodynamics and geophysical fluids. The Laplace and Fourier transform techniques are used to approximate the Riesz fractional operator in a spatial direction. The behaviors of the Helmholtz and Kelvin–Helmholtz equations are observed for some values of fractional power in the regimes,
0
<
α
≤
1
and
1
<
α
≤
2
, using different boundary conditions on a square domain in 1D, 2D and 3D (spatial-dimensions). Numerical results reveal some astonishing and very impressive phenomena which arise due to the variations in the initial and source function, as well as fractional parameter
α
, for subdiffusive and superdiffusive scenarios.</abstract><cop>Singapore</cop><pub>World Scientific Publishing Company</pub><doi>10.1142/S0218348X2240182X</doi><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| subjects | Boundary conditions Dynamic stability Fourier transforms Geophysical fluids Helmholtz equations Kelvin-Helmholtz instability Mathematical models Operators (mathematics) |
| title | CHAOTIC BEHAVIOR IN FRACTIONAL HELMHOLTZ AND KELVIN–HELMHOLTZ INSTABILITY PROBLEMS WITH RIESZ OPERATOR |
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