Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions
Abstract This paper is concerned with a class of impulsive implicit fractional integrodifferential equations having the boundary value problem with mixed Riemann–Liouville fractional integral boundary conditions. We establish some existence and uniqueness results for the given problem by applying th...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-02-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-020-2534-1 |
| _version_ | 1818453779069009920 |
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| author | Akbar Zada Jehad Alzabut Hira Waheed Ioan-Lucian Popa |
| author_facet | Akbar Zada Jehad Alzabut Hira Waheed Ioan-Lucian Popa |
| author_sort | Akbar Zada |
| collection | DOAJ |
| description | Abstract This paper is concerned with a class of impulsive implicit fractional integrodifferential equations having the boundary value problem with mixed Riemann–Liouville fractional integral boundary conditions. We establish some existence and uniqueness results for the given problem by applying the tools of fixed point theory. Furthermore, we investigate different kinds of stability such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability. Finally, we give two examples to demonstrate the validity of main results. |
| first_indexed | 2024-12-14T21:44:24Z |
| format | Article |
| id | doaj.art-5220ae81e1bf4c268a99ce9f289ce056 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-14T21:44:24Z |
| publishDate | 2020-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-5220ae81e1bf4c268a99ce9f289ce0562022-12-21T22:46:23ZengSpringerOpenAdvances in Difference Equations1687-18472020-02-012020115010.1186/s13662-020-2534-1Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditionsAkbar Zada0Jehad Alzabut1Hira Waheed2Ioan-Lucian Popa3Department of Mathematics, University of PeshawarDepartment of Mathematics and General Sciences, Prince Sultan UniversityDepartment of Mathematics, University of PeshawarDepartment of Exact Science and Engineering, “1 Decembrie 1918” University of Alba IuliaAbstract This paper is concerned with a class of impulsive implicit fractional integrodifferential equations having the boundary value problem with mixed Riemann–Liouville fractional integral boundary conditions. We establish some existence and uniqueness results for the given problem by applying the tools of fixed point theory. Furthermore, we investigate different kinds of stability such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability. Finally, we give two examples to demonstrate the validity of main results.https://doi.org/10.1186/s13662-020-2534-1Caputo derivativeRiemann–Liouville integralImpulseUlam–Hyers stabilityFixed point theory |
| spellingShingle | Akbar Zada Jehad Alzabut Hira Waheed Ioan-Lucian Popa Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions Advances in Difference Equations Caputo derivative Riemann–Liouville integral Impulse Ulam–Hyers stability Fixed point theory |
| title | Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions |
| title_full | Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions |
| title_fullStr | Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions |
| title_full_unstemmed | Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions |
| title_short | Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions |
| title_sort | ulam hyers stability of impulsive integrodifferential equations with riemann liouville boundary conditions |
| topic | Caputo derivative Riemann–Liouville integral Impulse Ulam–Hyers stability Fixed point theory |
| url | https://doi.org/10.1186/s13662-020-2534-1 |
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