New insight in fractional differentiation: power, exponential decay and Mittag-Leffler laws and applications
. Some physical problems found in nature can follow the power law; others can follow the Mittag-Leffler law and others the exponential decay law. On the other hand, one can observe in nature a physical problem that combines the three laws, it is therefore important to provide a new fractional operat...
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| Veröffentlicht in: | European physical journal plus 2017-01, Vol.132 (1), p.13, Article 13 |
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| creator | Gómez-Aguilar, J. F. Atangana, Abdon |
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Some physical problems found in nature can follow the power law; others can follow the Mittag-Leffler law and others the exponential decay law. On the other hand, one can observe in nature a physical problem that combines the three laws, it is therefore important to provide a new fractional operator that could possibly be used to model such physical problem. In this paper, we suggest a fractional operator power-law-exponential-Mittag-Leffler kernel with three fractional orders. Some very useful properties are obtained. Numerical solutions were obtained for three examples proposed. The results show that the new fractional operators are powerful mathematical tools to model complex problems. |
| doi_str_mv | 10.1140/epjp/i2017-11293-3 |
| format | Article |
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Some physical problems found in nature can follow the power law; others can follow the Mittag-Leffler law and others the exponential decay law. On the other hand, one can observe in nature a physical problem that combines the three laws, it is therefore important to provide a new fractional operator that could possibly be used to model such physical problem. In this paper, we suggest a fractional operator power-law-exponential-Mittag-Leffler kernel with three fractional orders. Some very useful properties are obtained. Numerical solutions were obtained for three examples proposed. The results show that the new fractional operators are powerful mathematical tools to model complex problems.</description><identifier>ISSN: 2190-5444</identifier><identifier>EISSN: 2190-5444</identifier><identifier>DOI: 10.1140/epjp/i2017-11293-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applied and Technical Physics ; Atomic ; Calculus ; Complex Systems ; Condensed Matter Physics ; Decay ; Mathematical and Computational Physics ; Mathematical functions ; Molecular ; Operators (mathematics) ; Optical and Plasma Physics ; Physics ; Physics and Astronomy ; Power ; Power law ; Regular Article ; Theoretical</subject><ispartof>European physical journal plus, 2017-01, Vol.132 (1), p.13, Article 13</ispartof><rights>Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2017</rights><rights>Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2017.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c319t-d7fd5e18c7ce6073dedbfcf96ddfdaed73555235e40c6bb1aad2b284098663773</citedby><cites>FETCH-LOGICAL-c319t-d7fd5e18c7ce6073dedbfcf96ddfdaed73555235e40c6bb1aad2b284098663773</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1140/epjp/i2017-11293-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2919897780?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,21388,27924,27925,33744,41488,42557,43805,51319,64385,64389,72469</link.rule.ids></links><search><creatorcontrib>Gómez-Aguilar, J. F.</creatorcontrib><creatorcontrib>Atangana, Abdon</creatorcontrib><title>New insight in fractional differentiation: power, exponential decay and Mittag-Leffler laws and applications</title><title>European physical journal plus</title><addtitle>Eur. Phys. J. Plus</addtitle><description>.
Some physical problems found in nature can follow the power law; others can follow the Mittag-Leffler law and others the exponential decay law. On the other hand, one can observe in nature a physical problem that combines the three laws, it is therefore important to provide a new fractional operator that could possibly be used to model such physical problem. In this paper, we suggest a fractional operator power-law-exponential-Mittag-Leffler kernel with three fractional orders. Some very useful properties are obtained. Numerical solutions were obtained for three examples proposed. The results show that the new fractional operators are powerful mathematical tools to model complex problems.</description><subject>Applied and Technical Physics</subject><subject>Atomic</subject><subject>Calculus</subject><subject>Complex Systems</subject><subject>Condensed Matter Physics</subject><subject>Decay</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical functions</subject><subject>Molecular</subject><subject>Operators (mathematics)</subject><subject>Optical and Plasma Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Power</subject><subject>Power law</subject><subject>Regular Article</subject><subject>Theoretical</subject><issn>2190-5444</issn><issn>2190-5444</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>AFKRA</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp9kEtPwzAQhC0EElXpH-AUiSuhfiWOuaGKl1TgAmfLsdfFVUiMnar035OmSHBiL7safTPSDkLnBF8RwvEcwjrMPcVE5IRQyXJ2hCaUSJwXnPPjP_cpmqW0xsNwSbjkE9Q8wzbzbfKr937YmYva9L5rdZNZ7xxEaHuv98p1FrotxMsMvkLXjvLAgNG7TLc2e_J9r1f5EpxrIGaN3qZR1yE03owJ6QydON0kmP3sKXq7u31dPOTLl_vHxc0yN4zIPrfC2QJIZYSBEgtmwdbOOFla66wGK1hRFJQVwLEp65pobWlNK45lVZZMCDZFF4fcELvPDaRerbtNHH5KikoiKylEhQeKHigTu5QiOBWi_9BxpwhW-2LVvlg1FqvGYhUbTOxgSgPcriD-Rv_j-gYuAn-8</recordid><startdate>20170101</startdate><enddate>20170101</enddate><creator>Gómez-Aguilar, J. 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F. ; Atangana, Abdon</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c319t-d7fd5e18c7ce6073dedbfcf96ddfdaed73555235e40c6bb1aad2b284098663773</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Applied and Technical Physics</topic><topic>Atomic</topic><topic>Calculus</topic><topic>Complex Systems</topic><topic>Condensed Matter Physics</topic><topic>Decay</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical functions</topic><topic>Molecular</topic><topic>Operators (mathematics)</topic><topic>Optical and Plasma Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Power</topic><topic>Power law</topic><topic>Regular Article</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gómez-Aguilar, J. 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Some physical problems found in nature can follow the power law; others can follow the Mittag-Leffler law and others the exponential decay law. On the other hand, one can observe in nature a physical problem that combines the three laws, it is therefore important to provide a new fractional operator that could possibly be used to model such physical problem. In this paper, we suggest a fractional operator power-law-exponential-Mittag-Leffler kernel with three fractional orders. Some very useful properties are obtained. Numerical solutions were obtained for three examples proposed. The results show that the new fractional operators are powerful mathematical tools to model complex problems.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1140/epjp/i2017-11293-3</doi></addata></record> |
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| subjects | Applied and Technical Physics Atomic Calculus Complex Systems Condensed Matter Physics Decay Mathematical and Computational Physics Mathematical functions Molecular Operators (mathematics) Optical and Plasma Physics Physics Physics and Astronomy Power Power law Regular Article Theoretical |
| title | New insight in fractional differentiation: power, exponential decay and Mittag-Leffler laws and applications |
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