Approximating fractional derivative of Faddeeva function, Gaussian function, and Dawson's integral
A new method for approximating fractional derivatives of Faddeeva function, Gaussian function, and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann‐Liouville integral over a finite interval using polynomial or discrete Fou...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2021-07, Vol.44 (10), p.8042-8056 |
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| creator | Yarman, Can Evren |
| description | A new method for approximating fractional derivatives of Faddeeva function, Gaussian function, and Dawson's integral are presented. Unlike previous approaches, which are dominantly based on some discretization of Riemann‐Liouville integral over a finite interval using polynomial or discrete Fourier basis, we take an alternative approach that is based on expressing computation of Riemann‐Liouville definition of the fractional integral for the semi‐infinite axis in terms of a moment problem. As a result, fractional derivatives of Faddeeva function, Gaussian function, and Dawson's integral are expressed as a weighted sum of complex scaled Gaussian and Dawson's integral. Error bounds for the approximations are provided. Another feature of the proposed method compared with the previous approaches is it can be extended to approximate partial derivatives with respect to the order of the fractional derivative that can be used in PDE constraint optimization problems. |
| doi_str_mv | 10.1002/mma.5679 |
| format | Article |
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Another feature of the proposed method compared with the previous approaches is it can be extended to approximate partial derivatives with respect to the order of the fractional derivative that can be used in PDE constraint optimization problems.</description><subject>26A33 fractional derivatives and integrals</subject><subject>33F05 numerical approximation and evaluation</subject><subject>44A60 moment problems</subject><subject>Approximation</subject><subject>Dawson</subject><subject>Derivatives</subject><subject>Faddeeva</subject><subject>Fractional calculus</subject><subject>Gaussian</subject><subject>Integrals</subject><subject>Liouville‐Caputo fractional derivative</subject><subject>Optimization</subject><subject>Polynomials</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLwzAYhoMoOKfgTwh40IOdSZo0zXFMN4UNL3oOaZOMjC6dSbu5f2-2efDi6ft4eXjheQG4xWiEESJP67UasYKLMzDASIgMU16cgwHCHGWUYHoJrmJcIYRKjMkAVOPNJrTfbq0655fQBlV3rvWqgdoEt03p1sDWwqnS2pitgrb3R-IRzlQfo1P-T6S8hs9qF1t_H6HznVkG1VyDC6uaaG5-7xB8Tl8-Jq_Z_H32NhnPs5qIXGSWGiIqoym2ulKEV6jWBDPGcEUJ49by9JScmdLqIs8FzYmuhRDUlLQQqWII7k69SeirN7GTq7YPSSVKwvKiyAUjJFEPJ6oObYzBWLkJyT7sJUbysKBMC8rDggnNTujONWb_LycXi_GR_wErcXI0</recordid><startdate>20210715</startdate><enddate>20210715</enddate><creator>Yarman, Can Evren</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0002-1612-6658</orcidid></search><sort><creationdate>20210715</creationdate><title>Approximating fractional derivative of Faddeeva function, Gaussian function, and Dawson's integral</title><author>Yarman, Can Evren</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2939-f4e29bed41fdba27b0cd215551b4257ff71b4875e8fd6339432dc9994e8469293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>26A33 fractional derivatives and integrals</topic><topic>33F05 numerical approximation and evaluation</topic><topic>44A60 moment problems</topic><topic>Approximation</topic><topic>Dawson</topic><topic>Derivatives</topic><topic>Faddeeva</topic><topic>Fractional calculus</topic><topic>Gaussian</topic><topic>Integrals</topic><topic>Liouville‐Caputo fractional derivative</topic><topic>Optimization</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yarman, Can Evren</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yarman, Can Evren</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Approximating fractional derivative of Faddeeva function, Gaussian function, and Dawson's integral</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2021-07-15</date><risdate>2021</risdate><volume>44</volume><issue>10</issue><spage>8042</spage><epage>8056</epage><pages>8042-8056</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>A new method for approximating fractional derivatives of Faddeeva function, Gaussian function, and Dawson's integral are presented. 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| language | eng |
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| source | Wiley Journals |
| subjects | 26A33 fractional derivatives and integrals 33F05 numerical approximation and evaluation 44A60 moment problems Approximation Dawson Derivatives Faddeeva Fractional calculus Gaussian Integrals Liouville‐Caputo fractional derivative Optimization Polynomials |
| title | Approximating fractional derivative of Faddeeva function, Gaussian function, and Dawson's integral |
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