On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditions
In this paper, we study a boundary value problem consisting of Hahn integro-difference equation supplemented with four-point fractional Hahn integral boundary conditions. The novelty of this problem lies in the fact that it contains two fractional Hahn difference operators and three fractional Hahn...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022040?viewType=HTML |
| _version_ | 1798035653066227712 |
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| author | Varaporn Wattanakejorn Sotiris K. Ntouyas Thanin Sitthiwirattham |
| author_facet | Varaporn Wattanakejorn Sotiris K. Ntouyas Thanin Sitthiwirattham |
| author_sort | Varaporn Wattanakejorn |
| collection | DOAJ |
| description | In this paper, we study a boundary value problem consisting of Hahn integro-difference equation supplemented with four-point fractional Hahn integral boundary conditions. The novelty of this problem lies in the fact that it contains two fractional Hahn difference operators and three fractional Hahn integrals with different quantum numbers and orders. Firstly, we convert the given nonlinear problem into a fixed point problem, by considering a linear variant of the problem at hand. Once the fixed point operator is available, we make use the classical Banach's and Schauder's fixed point theorems to establish existence and uniqueness results. An example is also constructed to illustrate the main results. Several properties of fractional Hahn integral that will be used in our study are also discussed. |
| first_indexed | 2024-04-11T21:00:20Z |
| format | Article |
| id | doaj.art-96b6720cd6f846b985a999afb4760440 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-11T21:00:20Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-96b6720cd6f846b985a999afb47604402022-12-22T04:03:31ZengAIMS PressAIMS Mathematics2473-69882022-01-017163265010.3934/math.2022040On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditionsVaraporn Wattanakejorn0Sotiris K. Ntouyas1Thanin Sitthiwirattham 21. Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand2. Department of Mathematics, University of Ioannina, Ioannina 45110, Greece 3. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia1. Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, ThailandIn this paper, we study a boundary value problem consisting of Hahn integro-difference equation supplemented with four-point fractional Hahn integral boundary conditions. The novelty of this problem lies in the fact that it contains two fractional Hahn difference operators and three fractional Hahn integrals with different quantum numbers and orders. Firstly, we convert the given nonlinear problem into a fixed point problem, by considering a linear variant of the problem at hand. Once the fixed point operator is available, we make use the classical Banach's and Schauder's fixed point theorems to establish existence and uniqueness results. An example is also constructed to illustrate the main results. Several properties of fractional Hahn integral that will be used in our study are also discussed.https://www.aimspress.com/article/doi/10.3934/math.2022040?viewType=HTMLfractional hahn integralfractional hahn differenceboundary value problemsexistence |
| spellingShingle | Varaporn Wattanakejorn Sotiris K. Ntouyas Thanin Sitthiwirattham On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditions AIMS Mathematics fractional hahn integral fractional hahn difference boundary value problems existence |
| title | On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditions |
| title_full | On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditions |
| title_fullStr | On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditions |
| title_full_unstemmed | On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditions |
| title_short | On a boundary value problem for fractional Hahn integro-difference equations with four-point fractional integral boundary conditions |
| title_sort | on a boundary value problem for fractional hahn integro difference equations with four point fractional integral boundary conditions |
| topic | fractional hahn integral fractional hahn difference boundary value problems existence |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022040?viewType=HTML |
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