Numerical solution of distributed order fractional differential equations by hybrid functions
In this paper, a new numerical method for solving the distributed fractional differential equations is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann–Liouv...
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| Veröffentlicht in: | Journal of computational physics 2016-06, Vol.315, p.169-181 |
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| container_title | Journal of computational physics |
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| creator | Mashayekhi, S. Razzaghi, M. |
| description | In this paper, a new numerical method for solving the distributed fractional differential equations is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann–Liouville fractional integral operator for hybrid functions is introduced. This operator is then utilized to reduce the solution of the distributed fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. |
| doi_str_mv | 10.1016/j.jcp.2016.01.041 |
| format | Article |
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Illustrative examples are included to demonstrate the validity and applicability of the technique.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/j.jcp.2016.01.041</identifier><language>eng</language><publisher>Elsevier Inc</publisher><subject>Algebra ; Approximation ; Bernoulli polynomials ; Blocking ; Caputo derivative ; Differential equations ; Distributed order ; Fractional differential equations ; Hybrid functions ; Mathematical analysis ; Mathematical models ; Numerical solution ; Operators ; Polynomials</subject><ispartof>Journal of computational physics, 2016-06, Vol.315, p.169-181</ispartof><rights>2016 Elsevier Inc.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c330t-5ad8a25d488595d49f4ccd7b5c3da7cf82b1a67aa913ab50dafb1dac8b6c49b63</citedby><cites>FETCH-LOGICAL-c330t-5ad8a25d488595d49f4ccd7b5c3da7cf82b1a67aa913ab50dafb1dac8b6c49b63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S002199911630016X$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>Mashayekhi, S.</creatorcontrib><creatorcontrib>Razzaghi, M.</creatorcontrib><title>Numerical solution of distributed order fractional differential equations by hybrid functions</title><title>Journal of computational physics</title><description>In this paper, a new numerical method for solving the distributed fractional differential equations is presented. 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Illustrative examples are included to demonstrate the validity and applicability of the technique.</description><subject>Algebra</subject><subject>Approximation</subject><subject>Bernoulli polynomials</subject><subject>Blocking</subject><subject>Caputo derivative</subject><subject>Differential equations</subject><subject>Distributed order</subject><subject>Fractional differential equations</subject><subject>Hybrid functions</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Numerical solution</subject><subject>Operators</subject><subject>Polynomials</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9kDtPwzAUhS0EEqXwA9g8siT4JnFiiwlVvKQKFhiR5adwlMatnSD13-NSZqZzH9-50j0IXQMpgUB725e93pZVLksCJWngBC2AcFJUHbSnaEFIBQXnHM7RRUo9IYTRhi3Q5-u8sdFrOeAUhnnyYcTBYePTFL2aJ2twiMZG7KLUh20GjXfORjtOPjd2N8vDPGG1x197Fb3Bbh5_2XSJzpwckr360yX6eHx4Xz0X67enl9X9utB1TaaCSsNkRU3DGOVZuGu0Np2iujay045VCmTbScmhlooSI50CIzVTrW64auslujne3cawm22axMYnbYdBjjbMSQADynlT0y6jcER1DClF68Q2-o2MewFEHKIUvchRikOUgoDIUWbP3dFj8w_f3kaRtLejtsZHqydhgv_H_QNki39G</recordid><startdate>20160615</startdate><enddate>20160615</enddate><creator>Mashayekhi, S.</creator><creator>Razzaghi, M.</creator><general>Elsevier Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20160615</creationdate><title>Numerical solution of distributed order fractional differential equations by hybrid functions</title><author>Mashayekhi, S. ; Razzaghi, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c330t-5ad8a25d488595d49f4ccd7b5c3da7cf82b1a67aa913ab50dafb1dac8b6c49b63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Algebra</topic><topic>Approximation</topic><topic>Bernoulli polynomials</topic><topic>Blocking</topic><topic>Caputo derivative</topic><topic>Differential equations</topic><topic>Distributed order</topic><topic>Fractional differential equations</topic><topic>Hybrid functions</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Numerical solution</topic><topic>Operators</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mashayekhi, S.</creatorcontrib><creatorcontrib>Razzaghi, M.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mashayekhi, S.</au><au>Razzaghi, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical solution of distributed order fractional differential equations by hybrid functions</atitle><jtitle>Journal of computational physics</jtitle><date>2016-06-15</date><risdate>2016</risdate><volume>315</volume><spage>169</spage><epage>181</epage><pages>169-181</pages><issn>0021-9991</issn><eissn>1090-2716</eissn><abstract>In this paper, a new numerical method for solving the distributed fractional differential equations is presented. 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| ispartof | Journal of computational physics, 2016-06, Vol.315, p.169-181 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Algebra Approximation Bernoulli polynomials Blocking Caputo derivative Differential equations Distributed order Fractional differential equations Hybrid functions Mathematical analysis Mathematical models Numerical solution Operators Polynomials |
| title | Numerical solution of distributed order fractional differential equations by hybrid functions |
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