On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations
In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The differ...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/4/476 |
| _version_ | 1797571860171325440 |
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| author | Jiraporn Reunsumrit Thanin Sitthiwirattham |
| author_facet | Jiraporn Reunsumrit Thanin Sitthiwirattham |
| author_sort | Jiraporn Reunsumrit |
| collection | DOAJ |
| description | In this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example. |
| first_indexed | 2024-03-10T20:46:41Z |
| format | Article |
| id | doaj.art-36002da844da4726a120700421ab3abf |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:46:41Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-36002da844da4726a120700421ab3abf2023-11-19T20:14:53ZengMDPI AGMathematics2227-73902020-03-018447610.3390/math8040476On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference EquationsJiraporn Reunsumrit0Thanin Sitthiwirattham1Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, ThailandMathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, ThailandIn this paper, we propose sequential fractional delta-nabla sum-difference equations with nonlocal fractional delta-nabla sum boundary conditions. The Banach contraction principle and the Schauder’s fixed point theorem are used to prove the existence and uniqueness results of the problem. The different orders in one fractional delta differences, one fractional nabla differences, two fractional delta sum, and two fractional nabla sum are considered. Finally, we present an illustrative example.https://www.mdpi.com/2227-7390/8/4/476sequential fractional delta-nabla sum-difference equationsnonlocal fractional delta-nabla sum boundary value problemexistenceuniqueness |
| spellingShingle | Jiraporn Reunsumrit Thanin Sitthiwirattham On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations Mathematics sequential fractional delta-nabla sum-difference equations nonlocal fractional delta-nabla sum boundary value problem existence uniqueness |
| title | On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations |
| title_full | On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations |
| title_fullStr | On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations |
| title_full_unstemmed | On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations |
| title_short | On the Nonlocal Fractional Delta-Nabla Sum Boundary Value Problem for Sequential Fractional Delta-Nabla Sum-Difference Equations |
| title_sort | on the nonlocal fractional delta nabla sum boundary value problem for sequential fractional delta nabla sum difference equations |
| topic | sequential fractional delta-nabla sum-difference equations nonlocal fractional delta-nabla sum boundary value problem existence uniqueness |
| url | https://www.mdpi.com/2227-7390/8/4/476 |
| work_keys_str_mv | AT jirapornreunsumrit onthenonlocalfractionaldeltanablasumboundaryvalueproblemforsequentialfractionaldeltanablasumdifferenceequations AT thaninsitthiwirattham onthenonlocalfractionaldeltanablasumboundaryvalueproblemforsequentialfractionaldeltanablasumdifferenceequations |