A study on Hilfer–Katugampola fractional differential equations with boundary conditions
Abstract In this paper, we investigate the existence of solutions of Hilfer-Katugampola fractional differential equations with boundary conditions. We first establish existence theory of solutions for the mentioned problem by the fixed point theory and the measure of noncompactness. Then we investig...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-024-01980-x |
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| _version_ | 1841559209972334592 |
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| author | Jing Zhang Haide Gou |
| author_facet | Jing Zhang Haide Gou |
| author_sort | Jing Zhang |
| collection | DOAJ |
| description | Abstract In this paper, we investigate the existence of solutions of Hilfer-Katugampola fractional differential equations with boundary conditions. We first establish existence theory of solutions for the mentioned problem by the fixed point theory and the measure of noncompactness. Then we investigate the ε-approximate solution to our concerned problem via a generalized Gronwall inequality. Finally, as the application of abstract results, we give an example to illustrate our main results. |
| format | Article |
| id | doaj-art-5919121a09a2402cbf203bd90578cbcb |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-5919121a09a2402cbf203bd90578cbcb2025-01-05T12:41:50ZengSpringerOpenBoundary Value Problems1687-27702025-01-012025112310.1186/s13661-024-01980-xA study on Hilfer–Katugampola fractional differential equations with boundary conditionsJing Zhang0Haide Gou1College of Science, Gansu Agricultural UniversityCollege of Mathematics and Statistics, Northwest Normal UniversityAbstract In this paper, we investigate the existence of solutions of Hilfer-Katugampola fractional differential equations with boundary conditions. We first establish existence theory of solutions for the mentioned problem by the fixed point theory and the measure of noncompactness. Then we investigate the ε-approximate solution to our concerned problem via a generalized Gronwall inequality. Finally, as the application of abstract results, we give an example to illustrate our main results.https://doi.org/10.1186/s13661-024-01980-xHilfer–Katugampola fractional derivativeBoundary conditionsMönch fixed pointMeasure of noncompactnessε-approximate |
| spellingShingle | Jing Zhang Haide Gou A study on Hilfer–Katugampola fractional differential equations with boundary conditions Boundary Value Problems Hilfer–Katugampola fractional derivative Boundary conditions Mönch fixed point Measure of noncompactness ε-approximate |
| title | A study on Hilfer–Katugampola fractional differential equations with boundary conditions |
| title_full | A study on Hilfer–Katugampola fractional differential equations with boundary conditions |
| title_fullStr | A study on Hilfer–Katugampola fractional differential equations with boundary conditions |
| title_full_unstemmed | A study on Hilfer–Katugampola fractional differential equations with boundary conditions |
| title_short | A study on Hilfer–Katugampola fractional differential equations with boundary conditions |
| title_sort | study on hilfer katugampola fractional differential equations with boundary conditions |
| topic | Hilfer–Katugampola fractional derivative Boundary conditions Mönch fixed point Measure of noncompactness ε-approximate |
| url | https://doi.org/10.1186/s13661-024-01980-x |
| work_keys_str_mv | AT jingzhang astudyonhilferkatugampolafractionaldifferentialequationswithboundaryconditions AT haidegou astudyonhilferkatugampolafractionaldifferentialequationswithboundaryconditions AT jingzhang studyonhilferkatugampolafractionaldifferentialequationswithboundaryconditions AT haidegou studyonhilferkatugampolafractionaldifferentialequationswithboundaryconditions |