Solving systems of coupled nonlinear Atangana–Baleanu-type fractional differential equations
Abstract In this work, we investigate two types of boundary value problems for a system of coupled Atangana–Baleanu-type fractional differential equations with nonlocal boundary conditions. The fractional derivatives are applied to serve as a nonlocal and nonsingular kernel. The existence and unique...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-12-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-022-01684-0 |
| _version_ | 1828090321828839424 |
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| author | Hasanen A. Hammad Mohra Zayed |
| author_facet | Hasanen A. Hammad Mohra Zayed |
| author_sort | Hasanen A. Hammad |
| collection | DOAJ |
| description | Abstract In this work, we investigate two types of boundary value problems for a system of coupled Atangana–Baleanu-type fractional differential equations with nonlocal boundary conditions. The fractional derivatives are applied to serve as a nonlocal and nonsingular kernel. The existence and uniqueness of solutions for proposed problems using Krasnoselskii’s and Banach’s fixed-point approaches are established. Moreover, nonlinear analysis is used to build the Ulam–Hyers stability theory. Subsequently, we discuss two compelling examples to demonstrate the utility of our study. |
| first_indexed | 2024-04-11T05:55:04Z |
| format | Article |
| id | doaj.art-1de26bd42b5448e0854f62413bca5d9f |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-11T05:55:04Z |
| publishDate | 2022-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-1de26bd42b5448e0854f62413bca5d9f2022-12-22T04:41:55ZengSpringerOpenBoundary Value Problems1687-27702022-12-012022112910.1186/s13661-022-01684-0Solving systems of coupled nonlinear Atangana–Baleanu-type fractional differential equationsHasanen A. Hammad0Mohra Zayed1Department of Mathematics, Unaizah College of Sciences and Arts, Qassim UniversityMathematics Department, College of Science, King Khalid UniversityAbstract In this work, we investigate two types of boundary value problems for a system of coupled Atangana–Baleanu-type fractional differential equations with nonlocal boundary conditions. The fractional derivatives are applied to serve as a nonlocal and nonsingular kernel. The existence and uniqueness of solutions for proposed problems using Krasnoselskii’s and Banach’s fixed-point approaches are established. Moreover, nonlinear analysis is used to build the Ulam–Hyers stability theory. Subsequently, we discuss two compelling examples to demonstrate the utility of our study.https://doi.org/10.1186/s13661-022-01684-0Atangana–Baleanu-typeFractional differential equationFixed point techniqueBoundary value problemUlam–Hyers stability |
| spellingShingle | Hasanen A. Hammad Mohra Zayed Solving systems of coupled nonlinear Atangana–Baleanu-type fractional differential equations Boundary Value Problems Atangana–Baleanu-type Fractional differential equation Fixed point technique Boundary value problem Ulam–Hyers stability |
| title | Solving systems of coupled nonlinear Atangana–Baleanu-type fractional differential equations |
| title_full | Solving systems of coupled nonlinear Atangana–Baleanu-type fractional differential equations |
| title_fullStr | Solving systems of coupled nonlinear Atangana–Baleanu-type fractional differential equations |
| title_full_unstemmed | Solving systems of coupled nonlinear Atangana–Baleanu-type fractional differential equations |
| title_short | Solving systems of coupled nonlinear Atangana–Baleanu-type fractional differential equations |
| title_sort | solving systems of coupled nonlinear atangana baleanu type fractional differential equations |
| topic | Atangana–Baleanu-type Fractional differential equation Fixed point technique Boundary value problem Ulam–Hyers stability |
| url | https://doi.org/10.1186/s13661-022-01684-0 |
| work_keys_str_mv | AT hasanenahammad solvingsystemsofcouplednonlinearatanganabaleanutypefractionaldifferentialequations AT mohrazayed solvingsystemsofcouplednonlinearatanganabaleanutypefractionaldifferentialequations |