Fractional Mixed Weighted Convolution and Its Application in Convolution Integral Equations
The convolution integral equations are very important in optics and signal processing domain. In this paper, fractional mixed-weighted convolution is defined based on the fractional cosine transform; the corresponding convolution theorem is achieved. The properties of fractional mixed-weighted convo...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/5375401 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832558666188849152 |
|---|---|
| author | Rongbo Wang Qiang Feng |
| author_facet | Rongbo Wang Qiang Feng |
| author_sort | Rongbo Wang |
| collection | DOAJ |
| description | The convolution integral equations are very important in optics and signal processing domain. In this paper, fractional mixed-weighted convolution is defined based on the fractional cosine transform; the corresponding convolution theorem is achieved. The properties of fractional mixed-weighted convolution and Young’s type theorem are also explored. Based on the fractional mixed-weighted convolution and fractional cosine transform, two kinds of convolution integral equations are considered, the explicit solutions of fractional convolution integral equations are obtained, and the computational complexity of solutions are also analyzed. |
| format | Article |
| id | doaj-art-7b7530ce9c38470195917133db657aca |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-7b7530ce9c38470195917133db657aca2025-02-03T01:31:53ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/5375401Fractional Mixed Weighted Convolution and Its Application in Convolution Integral EquationsRongbo Wang0Qiang Feng1School of Mathematics and Computer ScienceSchool of Mathematics and Computer ScienceThe convolution integral equations are very important in optics and signal processing domain. In this paper, fractional mixed-weighted convolution is defined based on the fractional cosine transform; the corresponding convolution theorem is achieved. The properties of fractional mixed-weighted convolution and Young’s type theorem are also explored. Based on the fractional mixed-weighted convolution and fractional cosine transform, two kinds of convolution integral equations are considered, the explicit solutions of fractional convolution integral equations are obtained, and the computational complexity of solutions are also analyzed.http://dx.doi.org/10.1155/2024/5375401 |
| spellingShingle | Rongbo Wang Qiang Feng Fractional Mixed Weighted Convolution and Its Application in Convolution Integral Equations Journal of Mathematics |
| title | Fractional Mixed Weighted Convolution and Its Application in Convolution Integral Equations |
| title_full | Fractional Mixed Weighted Convolution and Its Application in Convolution Integral Equations |
| title_fullStr | Fractional Mixed Weighted Convolution and Its Application in Convolution Integral Equations |
| title_full_unstemmed | Fractional Mixed Weighted Convolution and Its Application in Convolution Integral Equations |
| title_short | Fractional Mixed Weighted Convolution and Its Application in Convolution Integral Equations |
| title_sort | fractional mixed weighted convolution and its application in convolution integral equations |
| url | http://dx.doi.org/10.1155/2024/5375401 |
| work_keys_str_mv | AT rongbowang fractionalmixedweightedconvolutionanditsapplicationinconvolutionintegralequations AT qiangfeng fractionalmixedweightedconvolutionanditsapplicationinconvolutionintegralequations |