Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions
Abstract In this article, we investigate the existence and uniqueness of solutions for conformable derivatives in the Caputo setting with four-point integral conditions, applying standard fixed point theorems such as Banach contraction mapping principle, Krasnoselskii’s fixed point theorem, and Lera...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-04-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2077-5 |
| _version_ | 1818808420029956096 |
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| author | Aphirak Aphithana Sotiris K. Ntouyas Jessada Tariboon |
| author_facet | Aphirak Aphithana Sotiris K. Ntouyas Jessada Tariboon |
| author_sort | Aphirak Aphithana |
| collection | DOAJ |
| description | Abstract In this article, we investigate the existence and uniqueness of solutions for conformable derivatives in the Caputo setting with four-point integral conditions, applying standard fixed point theorems such as Banach contraction mapping principle, Krasnoselskii’s fixed point theorem, and Leray–Schauder nonlinear alternative. Further, we present Ulam–Hyers stability results by using direct analysis methods. Different types of Ulam stability, such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability, are studied. Examples which support our theoretical results are also presented. |
| first_indexed | 2024-12-18T19:41:16Z |
| format | Article |
| id | doaj.art-26ab8e96c05e4b308bc3aaa978574330 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-18T19:41:16Z |
| publishDate | 2019-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-26ab8e96c05e4b308bc3aaa9785743302022-12-21T20:55:26ZengSpringerOpenAdvances in Difference Equations1687-18472019-04-012019111710.1186/s13662-019-2077-5Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditionsAphirak Aphithana0Sotiris K. Ntouyas1Jessada Tariboon2Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North BangkokDepartment of Mathematics, University of IoanninaIntelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North BangkokAbstract In this article, we investigate the existence and uniqueness of solutions for conformable derivatives in the Caputo setting with four-point integral conditions, applying standard fixed point theorems such as Banach contraction mapping principle, Krasnoselskii’s fixed point theorem, and Leray–Schauder nonlinear alternative. Further, we present Ulam–Hyers stability results by using direct analysis methods. Different types of Ulam stability, such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability, are studied. Examples which support our theoretical results are also presented.http://link.springer.com/article/10.1186/s13662-019-2077-5Existence and uniquenessFixed point theoremFractional differential equationsConformable integralsConformable derivativesUlam–Hyers stability |
| spellingShingle | Aphirak Aphithana Sotiris K. Ntouyas Jessada Tariboon Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions Advances in Difference Equations Existence and uniqueness Fixed point theorem Fractional differential equations Conformable integrals Conformable derivatives Ulam–Hyers stability |
| title | Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions |
| title_full | Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions |
| title_fullStr | Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions |
| title_full_unstemmed | Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions |
| title_short | Existence and Ulam–Hyers stability for Caputo conformable differential equations with four-point integral conditions |
| title_sort | existence and ulam hyers stability for caputo conformable differential equations with four point integral conditions |
| topic | Existence and uniqueness Fixed point theorem Fractional differential equations Conformable integrals Conformable derivatives Ulam–Hyers stability |
| url | http://link.springer.com/article/10.1186/s13662-019-2077-5 |
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