On Lr-norm-based derivatives and fuzzy Henstock-Kurzweil integrals with an application
The fundamental theorem of calculus not only plays an important role in the study of differential equation theory, but also in many practical problems solving. In order to enrich its content, in present paper, we extend fuzzy derivatives and fuzzy Henstock-Kurzweil integrals. Firstly, we discuss som...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2023-03-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S111001682200802X |
| _version_ | 1797884456471625728 |
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| author | Yabin Shao Yubing Li Zengtai Gong |
| author_facet | Yabin Shao Yubing Li Zengtai Gong |
| author_sort | Yabin Shao |
| collection | DOAJ |
| description | The fundamental theorem of calculus not only plays an important role in the study of differential equation theory, but also in many practical problems solving. In order to enrich its content, in present paper, we extend fuzzy derivatives and fuzzy Henstock-Kurzweil integrals. Firstly, we discuss some properties of Lr-norm-based derivatives for fuzzy Henstock-Kurzweil integrable function (or briefly FLr-derivative). Then, we give some relationships with well-known fuzzy derivatives. After that, we also define a kind of fuzzy Henstock-Kurzweil integral based on FLr-derivative (or briefly Lr-FHK-integral). In addition, we give some important properties and convergence theorems for the Lr-FHK-integral. Meanwhile, we obtain a sufficient and necessary condition for integrability of this integral. As the application, we discuss the fuzzy Fourier series. |
| first_indexed | 2024-04-10T04:07:59Z |
| format | Article |
| id | doaj.art-1b49d16a54db4e17b30c1ba034c63ab2 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-10T04:07:59Z |
| publishDate | 2023-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-1b49d16a54db4e17b30c1ba034c63ab22023-03-13T04:15:13ZengElsevierAlexandria Engineering Journal1110-01682023-03-0167361373On Lr-norm-based derivatives and fuzzy Henstock-Kurzweil integrals with an applicationYabin Shao0Yubing Li1Zengtai Gong2School of Science, Chongqing University of Posts and Telecommunications, Nanan 400065, Chongqing, ChinaSchool of Science, Chongqing University of Posts and Telecommunications, Nanan 400065, Chongqing, ChinaCorresponding author.; School of Science, Chongqing University of Posts and Telecommunications, Nanan 400065, Chongqing, ChinaThe fundamental theorem of calculus not only plays an important role in the study of differential equation theory, but also in many practical problems solving. In order to enrich its content, in present paper, we extend fuzzy derivatives and fuzzy Henstock-Kurzweil integrals. Firstly, we discuss some properties of Lr-norm-based derivatives for fuzzy Henstock-Kurzweil integrable function (or briefly FLr-derivative). Then, we give some relationships with well-known fuzzy derivatives. After that, we also define a kind of fuzzy Henstock-Kurzweil integral based on FLr-derivative (or briefly Lr-FHK-integral). In addition, we give some important properties and convergence theorems for the Lr-FHK-integral. Meanwhile, we obtain a sufficient and necessary condition for integrability of this integral. As the application, we discuss the fuzzy Fourier series.http://www.sciencedirect.com/science/article/pii/S111001682200802X03E7226E5034A0734D20 |
| spellingShingle | Yabin Shao Yubing Li Zengtai Gong On Lr-norm-based derivatives and fuzzy Henstock-Kurzweil integrals with an application Alexandria Engineering Journal 03E72 26E50 34A07 34D20 |
| title | On Lr-norm-based derivatives and fuzzy Henstock-Kurzweil integrals with an application |
| title_full | On Lr-norm-based derivatives and fuzzy Henstock-Kurzweil integrals with an application |
| title_fullStr | On Lr-norm-based derivatives and fuzzy Henstock-Kurzweil integrals with an application |
| title_full_unstemmed | On Lr-norm-based derivatives and fuzzy Henstock-Kurzweil integrals with an application |
| title_short | On Lr-norm-based derivatives and fuzzy Henstock-Kurzweil integrals with an application |
| title_sort | on lr norm based derivatives and fuzzy henstock kurzweil integrals with an application |
| topic | 03E72 26E50 34A07 34D20 |
| url | http://www.sciencedirect.com/science/article/pii/S111001682200802X |
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