The weighted generalized Atangana-Baleanu fractional derivative in banach spaces- definition and applications
In this paper, we introduce the concept of the weighted generalized Atangana-Baleanu fractional derivative. We prove the existence of the stability of solutions of non-local differential equations and non-local differential inclusions, in Banach spaces, with this new fractional derivative in the pre...
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241722 |
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| author | Muneerah AL Nuwairan Ahmed Gamal Ibrahim |
| author_facet | Muneerah AL Nuwairan Ahmed Gamal Ibrahim |
| author_sort | Muneerah AL Nuwairan |
| collection | DOAJ |
| description | In this paper, we introduce the concept of the weighted generalized Atangana-Baleanu fractional derivative. We prove the existence of the stability of solutions of non-local differential equations and non-local differential inclusions, in Banach spaces, with this new fractional derivative in the presence of instantaneous and non-instantaneous impulses. We considered the case in which the lower limit of the fractional derivative was kept at the initial point and where it was changed to the impulsive points. To prove our results, we established the relationship between solutions to each of the four studied problems and those of the corresponding fractional integral equation. There has been no previous study of the weighted generalized Atangana-Baleanu fractional derivative, and so, our findings are new and interesting. The technique we used based on the properties of this new fractional differential operator and suitable fixed point theorems for single valued and set valued functions. Examples are given to illustrate the theoretical results. |
| format | Article |
| id | doaj-art-9fa6f2251b2545b88ca5f4e2de6f0908 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-9fa6f2251b2545b88ca5f4e2de6f09082025-01-23T07:53:26ZengAIMS PressAIMS Mathematics2473-69882024-12-01912362933633510.3934/math.20241722The weighted generalized Atangana-Baleanu fractional derivative in banach spaces- definition and applicationsMuneerah AL Nuwairan0Ahmed Gamal Ibrahim1Department of Mathematics, College of Sciences, King Faisal university, P.O.Box. 400, Al-Ahsa 31982, Saudi ArabiaDepartment of Mathematics, College of Sciences, Cairo University, EgyptIn this paper, we introduce the concept of the weighted generalized Atangana-Baleanu fractional derivative. We prove the existence of the stability of solutions of non-local differential equations and non-local differential inclusions, in Banach spaces, with this new fractional derivative in the presence of instantaneous and non-instantaneous impulses. We considered the case in which the lower limit of the fractional derivative was kept at the initial point and where it was changed to the impulsive points. To prove our results, we established the relationship between solutions to each of the four studied problems and those of the corresponding fractional integral equation. There has been no previous study of the weighted generalized Atangana-Baleanu fractional derivative, and so, our findings are new and interesting. The technique we used based on the properties of this new fractional differential operator and suitable fixed point theorems for single valued and set valued functions. Examples are given to illustrate the theoretical results.https://www.aimspress.com/article/doi/10.3934/math.20241722fractional differential equationsinclusions, instantaneous impulsesmeasure of noncompactness |
| spellingShingle | Muneerah AL Nuwairan Ahmed Gamal Ibrahim The weighted generalized Atangana-Baleanu fractional derivative in banach spaces- definition and applications AIMS Mathematics fractional differential equations inclusions, instantaneous impulses measure of noncompactness |
| title | The weighted generalized Atangana-Baleanu fractional derivative in banach spaces- definition and applications |
| title_full | The weighted generalized Atangana-Baleanu fractional derivative in banach spaces- definition and applications |
| title_fullStr | The weighted generalized Atangana-Baleanu fractional derivative in banach spaces- definition and applications |
| title_full_unstemmed | The weighted generalized Atangana-Baleanu fractional derivative in banach spaces- definition and applications |
| title_short | The weighted generalized Atangana-Baleanu fractional derivative in banach spaces- definition and applications |
| title_sort | weighted generalized atangana baleanu fractional derivative in banach spaces definition and applications |
| topic | fractional differential equations inclusions, instantaneous impulses measure of noncompactness |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241722 |
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