On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces
The generalization of BVPs always covers a wide range of equations. Our choice in this research is the generalization of Caputo-type fractional discrete differential equations that include two or more fractional q-integrals. We analyze the existence and uniqueness of solutions to the multi-point non...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Heliyon |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844024169071 |
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| author | Isra Al-Shbeil Houari Bouzid Benali Abdelkader Alina Alp Lupas Mohammad Esmael Samei Reem K. Alhefthi |
| author_facet | Isra Al-Shbeil Houari Bouzid Benali Abdelkader Alina Alp Lupas Mohammad Esmael Samei Reem K. Alhefthi |
| author_sort | Isra Al-Shbeil |
| collection | DOAJ |
| description | The generalization of BVPs always covers a wide range of equations. Our choice in this research is the generalization of Caputo-type fractional discrete differential equations that include two or more fractional q-integrals. We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVPs base on fixed point theory, including fixed point theorem of Banach, Leray-nonlinear Schauder's alternative, and Leray-degree Schauder's theory. Finally, several examples are presented to demonstrate accuracy of our results. |
| format | Article |
| id | doaj-art-12711026d82047118fcc79ac3323307a |
| institution | Kabale University |
| issn | 2405-8440 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj-art-12711026d82047118fcc79ac3323307a2025-01-17T04:49:50ZengElsevierHeliyon2405-84402025-01-01111e40876On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spacesIsra Al-Shbeil0Houari Bouzid1Benali Abdelkader2Alina Alp Lupas3Mohammad Esmael Samei4Reem K. Alhefthi5Department of Mathematics, Faculty of Sciences, The University of Jordan, 11942 Amman, Jordan; Corresponding author.Department of Mathematics, Faculty of Exact Science and Informatics, Hassiba Benbouali University of Chlef, Ouled Fares, Chlef 02000, Laboratory of Mathematics and Applications (LMA), AlgeriaDepartment of Mathematics, Faculty of Exact Science and Informatics, Hassiba Benbouali University of Chlef, Ouled Fares, Chlef 02000, Laboratory of Mathematics and Applications (LMA), AlgeriaDepartment of Mathematics and Computer Sciences, University of Oradea, 10087 Oradea, RomaniaDepartment of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, IranDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaThe generalization of BVPs always covers a wide range of equations. Our choice in this research is the generalization of Caputo-type fractional discrete differential equations that include two or more fractional q-integrals. We analyze the existence and uniqueness of solutions to the multi-point nonlinear BVPs base on fixed point theory, including fixed point theorem of Banach, Leray-nonlinear Schauder's alternative, and Leray-degree Schauder's theory. Finally, several examples are presented to demonstrate accuracy of our results.http://www.sciencedirect.com/science/article/pii/S2405844024169071Nonliner fractional equationLeray-Shauders alternativeExistenceq-R-L integral |
| spellingShingle | Isra Al-Shbeil Houari Bouzid Benali Abdelkader Alina Alp Lupas Mohammad Esmael Samei Reem K. Alhefthi On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces Heliyon Nonliner fractional equation Leray-Shauders alternative Existence q-R-L integral |
| title | On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces |
| title_full | On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces |
| title_fullStr | On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces |
| title_full_unstemmed | On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces |
| title_short | On the existence of solutions to fractional differential equations involving Caputo q-derivative in Banach spaces |
| title_sort | on the existence of solutions to fractional differential equations involving caputo q derivative in banach spaces |
| topic | Nonliner fractional equation Leray-Shauders alternative Existence q-R-L integral |
| url | http://www.sciencedirect.com/science/article/pii/S2405844024169071 |
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