On the Fractional Derivative of Dirac Delta Function and Its Application
The Dirac delta function and its integer-order derivative are widely used to solve integer-order differential/integral equation and integer-order system in related fields. On the other hand, the fractional-order system gets more and more attention. This paper investigates the fractional derivative o...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/1842945 |
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| _version_ | 1832567858360483840 |
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| author | Zaiyong Feng Linghua Ye Yi Zhang |
| author_facet | Zaiyong Feng Linghua Ye Yi Zhang |
| author_sort | Zaiyong Feng |
| collection | DOAJ |
| description | The Dirac delta function and its integer-order derivative are widely used to solve integer-order differential/integral equation and integer-order system in related fields. On the other hand, the fractional-order system gets more and more attention. This paper investigates the fractional derivative of the Dirac delta function and its Laplace transform to explore the solution for fractional-order system. The paper presents the Riemann-Liouville and the Caputo fractional derivative of the Dirac delta function, and their analytic expression. The Laplace transform of the fractional derivative of the Dirac delta function is given later. The proposed fractional derivative of the Dirac delta function and its Laplace transform are effectively used to solve fractional-order integral equation and fractional-order system, the correctness of each solution is also verified. |
| format | Article |
| id | doaj-art-418f339a152a4d0b9e208cbdca89a404 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-418f339a152a4d0b9e208cbdca89a4042025-02-03T01:00:18ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/18429451842945On the Fractional Derivative of Dirac Delta Function and Its ApplicationZaiyong Feng0Linghua Ye1Yi Zhang2Department of Mathematics Teaching, Nanjing Institute of Railway Technology, Nanjing 210031, ChinaDepartment of Finance, Nanjing Institute of Railway Technology, Nanjing 210031, ChinaDepartment of Mathematics Teaching, Nanjing Institute of Railway Technology, Nanjing 210031, ChinaThe Dirac delta function and its integer-order derivative are widely used to solve integer-order differential/integral equation and integer-order system in related fields. On the other hand, the fractional-order system gets more and more attention. This paper investigates the fractional derivative of the Dirac delta function and its Laplace transform to explore the solution for fractional-order system. The paper presents the Riemann-Liouville and the Caputo fractional derivative of the Dirac delta function, and their analytic expression. The Laplace transform of the fractional derivative of the Dirac delta function is given later. The proposed fractional derivative of the Dirac delta function and its Laplace transform are effectively used to solve fractional-order integral equation and fractional-order system, the correctness of each solution is also verified.http://dx.doi.org/10.1155/2020/1842945 |
| spellingShingle | Zaiyong Feng Linghua Ye Yi Zhang On the Fractional Derivative of Dirac Delta Function and Its Application Advances in Mathematical Physics |
| title | On the Fractional Derivative of Dirac Delta Function and Its Application |
| title_full | On the Fractional Derivative of Dirac Delta Function and Its Application |
| title_fullStr | On the Fractional Derivative of Dirac Delta Function and Its Application |
| title_full_unstemmed | On the Fractional Derivative of Dirac Delta Function and Its Application |
| title_short | On the Fractional Derivative of Dirac Delta Function and Its Application |
| title_sort | on the fractional derivative of dirac delta function and its application |
| url | http://dx.doi.org/10.1155/2020/1842945 |
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