Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order
This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation o...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2013/806984 |
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| author | Ming Li Wei Zhao |
| author_facet | Ming Li Wei Zhao |
| author_sort | Ming Li |
| collection | DOAJ |
| description | This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type. |
| format | Article |
| id | doaj-art-8f5eebf3507747bea53941278f45489d |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-8f5eebf3507747bea53941278f45489d2025-02-03T01:26:24ZengWileyAdvances in Mathematical Physics1687-91201687-91392013-01-01201310.1155/2013/806984806984Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional OrderMing Li0Wei Zhao1School of Information Science & Technology, East China Normal University, No. 500, Dong-Chuan Road, Shanghai 200241, ChinaDepartment of Computer and Information Science, University of Macau, Avenida Padre Tomas Pereira, Taipa, MacauThis paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type.http://dx.doi.org/10.1155/2013/806984 |
| spellingShingle | Ming Li Wei Zhao Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order Advances in Mathematical Physics |
| title | Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order |
| title_full | Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order |
| title_fullStr | Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order |
| title_full_unstemmed | Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order |
| title_short | Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order |
| title_sort | solving abel s type integral equation with mikusinski s operator of fractional order |
| url | http://dx.doi.org/10.1155/2013/806984 |
| work_keys_str_mv | AT mingli solvingabelstypeintegralequationwithmikusinskisoperatoroffractionalorder AT weizhao solvingabelstypeintegralequationwithmikusinskisoperatoroffractionalorder |