Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation
Abstract Fractional difference equations have become important due to their qualitative properties and applications in discrete modeling. Stability analysis of solutions is one of the most widely used qualitative properties with tremendous applications. In this paper, we investigate the existence an...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-05-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02674-1 |
| _version_ | 1818242961870159872 |
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| author | Rabia Ilyas Butt Thabet Abdeljawad Mujeeb ur Rehman |
| author_facet | Rabia Ilyas Butt Thabet Abdeljawad Mujeeb ur Rehman |
| author_sort | Rabia Ilyas Butt |
| collection | DOAJ |
| description | Abstract Fractional difference equations have become important due to their qualitative properties and applications in discrete modeling. Stability analysis of solutions is one of the most widely used qualitative properties with tremendous applications. In this paper, we investigate the existence and stability results for a class of non-linear Caputo nabla fractional difference equations. To obtain the existence and stability results, we use Schauder’s fixed point theorem, the Banach contraction principle and Krasnoselskii’s fixed point theorem. The analysis of the theoretical results depends on the structure of nabla discrete Mittag-Leffler functions. An example is provided to illustrate the theoretical results. |
| first_indexed | 2024-12-12T13:53:33Z |
| format | Article |
| id | doaj.art-4501473c056b416f8c23dc36816d8a18 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T13:53:33Z |
| publishDate | 2020-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4501473c056b416f8c23dc36816d8a182022-12-22T00:22:31ZengSpringerOpenAdvances in Difference Equations1687-18472020-05-012020111110.1186/s13662-020-02674-1Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equationRabia Ilyas Butt0Thabet Abdeljawad1Mujeeb ur Rehman2Department of Mathematics, School of Natural Sciences, National University of Sciences and TechnologyDepartment of Mathematics and General Sciences, Prince Sultan UniversityDepartment of Mathematics, School of Natural Sciences, National University of Sciences and TechnologyAbstract Fractional difference equations have become important due to their qualitative properties and applications in discrete modeling. Stability analysis of solutions is one of the most widely used qualitative properties with tremendous applications. In this paper, we investigate the existence and stability results for a class of non-linear Caputo nabla fractional difference equations. To obtain the existence and stability results, we use Schauder’s fixed point theorem, the Banach contraction principle and Krasnoselskii’s fixed point theorem. The analysis of the theoretical results depends on the structure of nabla discrete Mittag-Leffler functions. An example is provided to illustrate the theoretical results.http://link.springer.com/article/10.1186/s13662-020-02674-1Caputo nabla fractional differenceStabilitySchauder’s fixed point theoremBanach contraction principleKrasnoselskii’s fixed point theorem |
| spellingShingle | Rabia Ilyas Butt Thabet Abdeljawad Mujeeb ur Rehman Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation Advances in Difference Equations Caputo nabla fractional difference Stability Schauder’s fixed point theorem Banach contraction principle Krasnoselskii’s fixed point theorem |
| title | Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation |
| title_full | Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation |
| title_fullStr | Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation |
| title_full_unstemmed | Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation |
| title_short | Stability analysis by fixed point theorems for a class of non-linear Caputo nabla fractional difference equation |
| title_sort | stability analysis by fixed point theorems for a class of non linear caputo nabla fractional difference equation |
| topic | Caputo nabla fractional difference Stability Schauder’s fixed point theorem Banach contraction principle Krasnoselskii’s fixed point theorem |
| url | http://link.springer.com/article/10.1186/s13662-020-02674-1 |
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