Discrete fractional order two-point boundary value problem with some relevant physical applications
Abstract The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contracti...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-09-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-020-02485-8 |
| _version_ | 1818622924437848064 |
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| author | A. George Maria Selvam Jehad Alzabut R. Dhineshbabu S. Rashid M. Rehman |
| author_facet | A. George Maria Selvam Jehad Alzabut R. Dhineshbabu S. Rashid M. Rehman |
| author_sort | A. George Maria Selvam |
| collection | DOAJ |
| description | Abstract The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed. |
| first_indexed | 2024-12-16T18:32:54Z |
| format | Article |
| id | doaj.art-270365fc05d5433c8f82cc784c0a4ef4 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-16T18:32:54Z |
| publishDate | 2020-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-270365fc05d5433c8f82cc784c0a4ef42022-12-21T22:21:14ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-09-012020111910.1186/s13660-020-02485-8Discrete fractional order two-point boundary value problem with some relevant physical applicationsA. George Maria Selvam0Jehad Alzabut1R. Dhineshbabu2S. Rashid3M. Rehman4Department of Mathematics, Sacred Heart College (Autonomous)Department of Mathematics and General Sciences, Prince Sultan UniversityDepartment of Mathematics, Sacred Heart College (Autonomous)Department of Mathematics, Government College UniversitySchool of Natural Sciences, National University of Sciences and TechnologyAbstract The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed.http://link.springer.com/article/10.1186/s13660-020-02485-8Discrete boundary value problemDiscrete fractional calculusExistence and uniquenessUlam stabilityHeat equation |
| spellingShingle | A. George Maria Selvam Jehad Alzabut R. Dhineshbabu S. Rashid M. Rehman Discrete fractional order two-point boundary value problem with some relevant physical applications Journal of Inequalities and Applications Discrete boundary value problem Discrete fractional calculus Existence and uniqueness Ulam stability Heat equation |
| title | Discrete fractional order two-point boundary value problem with some relevant physical applications |
| title_full | Discrete fractional order two-point boundary value problem with some relevant physical applications |
| title_fullStr | Discrete fractional order two-point boundary value problem with some relevant physical applications |
| title_full_unstemmed | Discrete fractional order two-point boundary value problem with some relevant physical applications |
| title_short | Discrete fractional order two-point boundary value problem with some relevant physical applications |
| title_sort | discrete fractional order two point boundary value problem with some relevant physical applications |
| topic | Discrete boundary value problem Discrete fractional calculus Existence and uniqueness Ulam stability Heat equation |
| url | http://link.springer.com/article/10.1186/s13660-020-02485-8 |
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