Positive solutions for the Riemann–Liouville-type fractional differential equation system with infinite-point boundary conditions on infinite intervals
Abstract In this paper, we study the existence and uniqueness of positive solutions for a class of a fractional differential equation system of Riemann–Liouville type on infinite intervals with infinite-point boundary conditions. First, the higher-order equation is reduced to the lower-order equatio...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-03-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01850-6 |
| _version_ | 1797233471912935424 |
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| author | Yang Yu Qi Ge |
| author_facet | Yang Yu Qi Ge |
| author_sort | Yang Yu |
| collection | DOAJ |
| description | Abstract In this paper, we study the existence and uniqueness of positive solutions for a class of a fractional differential equation system of Riemann–Liouville type on infinite intervals with infinite-point boundary conditions. First, the higher-order equation is reduced to the lower-order equation, and then it is transformed into the equivalent integral equation. Secondly, we obtain the existence and uniqueness of positive solutions for each fixed parameter λ > 0 $\lambda >0$ by using the mixed monotone operators fixed-point theorem. The results obtained in this paper show that the unique positive solution has good properties: continuity, monotonicity, iteration, and approximation. Finally, an example is given to demonstrate the application of our main results. |
| first_indexed | 2024-04-24T16:16:42Z |
| format | Article |
| id | doaj.art-94613ed54fdb45b3aa5f7f271d5cf2fa |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-24T16:16:42Z |
| publishDate | 2024-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-94613ed54fdb45b3aa5f7f271d5cf2fa2024-03-31T11:27:07ZengSpringerOpenBoundary Value Problems1687-27702024-03-012024112010.1186/s13661-024-01850-6Positive solutions for the Riemann–Liouville-type fractional differential equation system with infinite-point boundary conditions on infinite intervalsYang Yu0Qi Ge1College of Science, Yanbian UniversityCollege of Science, Yanbian UniversityAbstract In this paper, we study the existence and uniqueness of positive solutions for a class of a fractional differential equation system of Riemann–Liouville type on infinite intervals with infinite-point boundary conditions. First, the higher-order equation is reduced to the lower-order equation, and then it is transformed into the equivalent integral equation. Secondly, we obtain the existence and uniqueness of positive solutions for each fixed parameter λ > 0 $\lambda >0$ by using the mixed monotone operators fixed-point theorem. The results obtained in this paper show that the unique positive solution has good properties: continuity, monotonicity, iteration, and approximation. Finally, an example is given to demonstrate the application of our main results.https://doi.org/10.1186/s13661-024-01850-6Fractional differential equation systemInfinite intervalsMixed monotone operatorsInfinite pointExistence and uniqueness of positive solutions |
| spellingShingle | Yang Yu Qi Ge Positive solutions for the Riemann–Liouville-type fractional differential equation system with infinite-point boundary conditions on infinite intervals Boundary Value Problems Fractional differential equation system Infinite intervals Mixed monotone operators Infinite point Existence and uniqueness of positive solutions |
| title | Positive solutions for the Riemann–Liouville-type fractional differential equation system with infinite-point boundary conditions on infinite intervals |
| title_full | Positive solutions for the Riemann–Liouville-type fractional differential equation system with infinite-point boundary conditions on infinite intervals |
| title_fullStr | Positive solutions for the Riemann–Liouville-type fractional differential equation system with infinite-point boundary conditions on infinite intervals |
| title_full_unstemmed | Positive solutions for the Riemann–Liouville-type fractional differential equation system with infinite-point boundary conditions on infinite intervals |
| title_short | Positive solutions for the Riemann–Liouville-type fractional differential equation system with infinite-point boundary conditions on infinite intervals |
| title_sort | positive solutions for the riemann liouville type fractional differential equation system with infinite point boundary conditions on infinite intervals |
| topic | Fractional differential equation system Infinite intervals Mixed monotone operators Infinite point Existence and uniqueness of positive solutions |
| url | https://doi.org/10.1186/s13661-024-01850-6 |
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