On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative
This work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order $ 0 < \theta < 1 $ in an arbitrary Banach space. We rely on some arguments to present the mild solution to our problem in terms of an $ \...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Emrah Evren KARA
2023-09-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/3104780 |
| _version_ | 1827381431241801728 |
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| author | Khalid Hilal Ahmed Kajounı Samira Zerbib |
| author_facet | Khalid Hilal Ahmed Kajounı Samira Zerbib |
| author_sort | Khalid Hilal |
| collection | DOAJ |
| description | This work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order $ 0 < \theta < 1 $ in an arbitrary Banach space. We rely on some arguments to present the mild solution to our problem in terms of an $ \theta $-resolvent family. Then we study the existence of this mild solution by using Krasnoselskii's fixed point theorem. Finally, we give an example to prove our results. |
| first_indexed | 2024-03-08T13:56:06Z |
| format | Article |
| id | doaj.art-683b600ec7994f10b7cfd7f2f30afab8 |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T13:56:06Z |
| publishDate | 2023-09-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-683b600ec7994f10b7cfd7f2f30afab82024-01-15T15:15:34ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532023-09-016312212910.32323/ujma.12880151225On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo DerivativeKhalid HilalAhmed Kajounı0Samira Zerbib1Sultan Moulay Slimane UniversitySultan Moulay Slimane UniversityThis work aims to study the existing results of mild solutions for a semi-linear Atangana-Baleanu-Caputo fractional differential equation with order $ 0 < \theta < 1 $ in an arbitrary Banach space. We rely on some arguments to present the mild solution to our problem in terms of an $ \theta $-resolvent family. Then we study the existence of this mild solution by using Krasnoselskii's fixed point theorem. Finally, we give an example to prove our results.https://dergipark.org.tr/tr/download/article-file/3104780atangana-baleanu-caputo derivativefractional semi-linear differential equationkrasnoselskii fixed point theoremresolvent family |
| spellingShingle | Khalid Hilal Ahmed Kajounı Samira Zerbib On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative Universal Journal of Mathematics and Applications atangana-baleanu-caputo derivative fractional semi-linear differential equation krasnoselskii fixed point theorem resolvent family |
| title | On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative |
| title_full | On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative |
| title_fullStr | On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative |
| title_full_unstemmed | On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative |
| title_short | On the Study of Semilinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative |
| title_sort | on the study of semilinear fractional differential equations involving atangana baleanu caputo derivative |
| topic | atangana-baleanu-caputo derivative fractional semi-linear differential equation krasnoselskii fixed point theorem resolvent family |
| url | https://dergipark.org.tr/tr/download/article-file/3104780 |
| work_keys_str_mv | AT khalidhilal onthestudyofsemilinearfractionaldifferentialequationsinvolvingatanganabaleanucaputoderivative AT ahmedkajounı onthestudyofsemilinearfractionaldifferentialequationsinvolvingatanganabaleanucaputoderivative AT samirazerbib onthestudyofsemilinearfractionaldifferentialequationsinvolvingatanganabaleanucaputoderivative |