On spectral methods for solving variable-order fractional integro-differential equations
This paper applies the shifted Jacobi–Gauss collocation (SJ–G-C) method for solving variable-order fractional integro-differential equations (VO-FIDE) with initial conditions. The Riemann–Liouville fractional derivative, D ν ( x ) , and integral, I ν ( x ) , of variable order are combined, and the S...
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| Veröffentlicht in: | Computation and applied mathematics 2018-07, Vol.37 (3), p.3937-3950 |
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| container_issue | 3 |
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| container_title | Computation and applied mathematics |
| container_volume | 37 |
| creator | Doha, E. H. Abdelkawy, M. A. Amin, A. Z. M. Lopes, António M. |
| description | This paper applies the shifted Jacobi–Gauss collocation (SJ–G-C) method for solving variable-order fractional integro-differential equations (VO-FIDE) with initial conditions. The Riemann–Liouville fractional derivative,
D
ν
(
x
)
, and integral,
I
ν
(
x
)
, of variable order are combined, and the SJ–G-C applied to produce a system of algebraic equations. Numerical experiments demonstrate the applicability and reliability of the algorithm when compared with current methods. |
| doi_str_mv | 10.1007/s40314-017-0551-9 |
| format | Article |
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D
ν
(
x
)
, and integral,
I
ν
(
x
)
, of variable order are combined, and the SJ–G-C applied to produce a system of algebraic equations. Numerical experiments demonstrate the applicability and reliability of the algorithm when compared with current methods.</description><identifier>ISSN: 0101-8205</identifier><identifier>ISSN: 2238-3603</identifier><identifier>EISSN: 1807-0302</identifier><identifier>DOI: 10.1007/s40314-017-0551-9</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>ALGORITHMS ; Applications of Mathematics ; Applied physics ; Computational mathematics ; Computational Mathematics and Numerical Analysis ; Derivatives ; Differential equations ; Initial conditions ; INTEGRALS ; INTEGRO-DIFFERENTIAL EQUATIONS ; Mathematical analysis ; Mathematical Applications in Computer Science ; Mathematical Applications in the Physical Sciences ; MATHEMATICAL METHODS AND COMPUTING ; Mathematics ; Mathematics and Statistics ; QUADRATURES ; RELIABILITY ; Spectral methods</subject><ispartof>Computation and applied mathematics, 2018-07, Vol.37 (3), p.3937-3950</ispartof><rights>SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017</rights><rights>Copyright Springer Science & Business Media 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c344t-74b7e8b94282e71b9d57a67174a2f3cf5ccfebd8123f39c7e24d2069dfc209ba3</citedby><cites>FETCH-LOGICAL-c344t-74b7e8b94282e71b9d57a67174a2f3cf5ccfebd8123f39c7e24d2069dfc209ba3</cites><orcidid>0000-0001-7359-4370</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40314-017-0551-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40314-017-0551-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,886,27929,27930,41493,42562,51324</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/22783793$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Doha, E. H.</creatorcontrib><creatorcontrib>Abdelkawy, M. A.</creatorcontrib><creatorcontrib>Amin, A. Z. M.</creatorcontrib><creatorcontrib>Lopes, António M.</creatorcontrib><title>On spectral methods for solving variable-order fractional integro-differential equations</title><title>Computation and applied mathematics</title><addtitle>Comp. Appl. Math</addtitle><description>This paper applies the shifted Jacobi–Gauss collocation (SJ–G-C) method for solving variable-order fractional integro-differential equations (VO-FIDE) with initial conditions. The Riemann–Liouville fractional derivative,
D
ν
(
x
)
, and integral,
I
ν
(
x
)
, of variable order are combined, and the SJ–G-C applied to produce a system of algebraic equations. Numerical experiments demonstrate the applicability and reliability of the algorithm when compared with current methods.</description><subject>ALGORITHMS</subject><subject>Applications of Mathematics</subject><subject>Applied physics</subject><subject>Computational mathematics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Derivatives</subject><subject>Differential equations</subject><subject>Initial conditions</subject><subject>INTEGRALS</subject><subject>INTEGRO-DIFFERENTIAL EQUATIONS</subject><subject>Mathematical analysis</subject><subject>Mathematical Applications in Computer Science</subject><subject>Mathematical Applications in the Physical Sciences</subject><subject>MATHEMATICAL METHODS AND COMPUTING</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>QUADRATURES</subject><subject>RELIABILITY</subject><subject>Spectral methods</subject><issn>0101-8205</issn><issn>2238-3603</issn><issn>1807-0302</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1UE1LAzEQDaJgqf0B3hY8Rycf22yOUvwCwYuCt5DNTtqUdtMmqeC_N6WCJ-cyzMx7b3iPkGsGtwxA3WUJgkkKTFFoW0b1GZmwDuokgJ-TCTBgtOPQXpJZzmuoJQEYn0_I59vY5B26kuym2WJZxSE3PqYmx81XGJfNl03B9hukMQ2YGp-sKyGOFR3GgssU6RC8x4RjCXWJ-4M93vMVufB2k3H226fk4_HhffFMX9-eXhb3r9QJKQtVslfY9VryjqNivR5aZeeKKWm5F863znnsh45x4YV2CrkcOMz14B0H3VsxJTcn3ZhLMNmFgm7l4jhWT4Zz1QmlxR9ql-L-gLmYdTyk6iKbqqY0Z7J-mBJ2QrkUc07ozS6FrU3fhoE5Jm1OSZuatDkmbXTl8BMnV-y4xPSn_D_pB8r_gQ4</recordid><startdate>20180701</startdate><enddate>20180701</enddate><creator>Doha, E. H.</creator><creator>Abdelkawy, M. A.</creator><creator>Amin, A. Z. M.</creator><creator>Lopes, António M.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope><orcidid>https://orcid.org/0000-0001-7359-4370</orcidid></search><sort><creationdate>20180701</creationdate><title>On spectral methods for solving variable-order fractional integro-differential equations</title><author>Doha, E. H. ; Abdelkawy, M. A. ; Amin, A. Z. M. ; Lopes, António M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c344t-74b7e8b94282e71b9d57a67174a2f3cf5ccfebd8123f39c7e24d2069dfc209ba3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>ALGORITHMS</topic><topic>Applications of Mathematics</topic><topic>Applied physics</topic><topic>Computational mathematics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Derivatives</topic><topic>Differential equations</topic><topic>Initial conditions</topic><topic>INTEGRALS</topic><topic>INTEGRO-DIFFERENTIAL EQUATIONS</topic><topic>Mathematical analysis</topic><topic>Mathematical Applications in Computer Science</topic><topic>Mathematical Applications in the Physical Sciences</topic><topic>MATHEMATICAL METHODS AND COMPUTING</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>QUADRATURES</topic><topic>RELIABILITY</topic><topic>Spectral methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Doha, E. H.</creatorcontrib><creatorcontrib>Abdelkawy, M. A.</creatorcontrib><creatorcontrib>Amin, A. Z. M.</creatorcontrib><creatorcontrib>Lopes, António M.</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Computation and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Doha, E. H.</au><au>Abdelkawy, M. A.</au><au>Amin, A. Z. M.</au><au>Lopes, António M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On spectral methods for solving variable-order fractional integro-differential equations</atitle><jtitle>Computation and applied mathematics</jtitle><stitle>Comp. Appl. Math</stitle><date>2018-07-01</date><risdate>2018</risdate><volume>37</volume><issue>3</issue><spage>3937</spage><epage>3950</epage><pages>3937-3950</pages><issn>0101-8205</issn><issn>2238-3603</issn><eissn>1807-0302</eissn><abstract>This paper applies the shifted Jacobi–Gauss collocation (SJ–G-C) method for solving variable-order fractional integro-differential equations (VO-FIDE) with initial conditions. The Riemann–Liouville fractional derivative,
D
ν
(
x
)
, and integral,
I
ν
(
x
)
, of variable order are combined, and the SJ–G-C applied to produce a system of algebraic equations. Numerical experiments demonstrate the applicability and reliability of the algorithm when compared with current methods.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40314-017-0551-9</doi><tpages>14</tpages><orcidid>https://orcid.org/0000-0001-7359-4370</orcidid></addata></record> |
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| source | SpringerNature Journals |
| subjects | ALGORITHMS Applications of Mathematics Applied physics Computational mathematics Computational Mathematics and Numerical Analysis Derivatives Differential equations Initial conditions INTEGRALS INTEGRO-DIFFERENTIAL EQUATIONS Mathematical analysis Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences MATHEMATICAL METHODS AND COMPUTING Mathematics Mathematics and Statistics QUADRATURES RELIABILITY Spectral methods |
| title | On spectral methods for solving variable-order fractional integro-differential equations |
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