Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions
In this article, we use some fixed point theorems to discuss the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation which involves Caputo fractional derivatives of different orders and is governed by new type of nonlocal and nonseparated boundary...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/3058414 |
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| author | Zaid Laadjal Qasem M. Al-Mdallal Fahd Jarad |
| author_facet | Zaid Laadjal Qasem M. Al-Mdallal Fahd Jarad |
| author_sort | Zaid Laadjal |
| collection | DOAJ |
| description | In this article, we use some fixed point theorems to discuss the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation which involves Caputo fractional derivatives of different orders and is governed by new type of nonlocal and nonseparated boundary conditions consisting of fractional integrals and derivatives. The considered boundary conditions are totally dissimilar than the ones already handled in the literature. Additionally, we modify the Adams-type predictor-corrector method by implicitly implementing the Gauss–Seidel method in order to solve some specific particular cases of the system. |
| format | Article |
| id | doaj-art-4bb967c24a0a44f48ea8a01aed9e0500 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4bb967c24a0a44f48ea8a01aed9e05002025-02-03T07:23:55ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/30584143058414Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary ConditionsZaid Laadjal0Qasem M. Al-Mdallal1Fahd Jarad2Department of Mathematics and Computer Sciences, ICOSI Laboratory, Abbes Laghrour University, Khenchela 40004, AlgeriaDepartment of Mathematical Sciences, United Arab Emirates University, P. O. Box 15551, Al Ain, Abu Dhabi, UAEDepartment of Mathematics, Çankaya University, Etimesgut, Ankara, TurkeyIn this article, we use some fixed point theorems to discuss the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation which involves Caputo fractional derivatives of different orders and is governed by new type of nonlocal and nonseparated boundary conditions consisting of fractional integrals and derivatives. The considered boundary conditions are totally dissimilar than the ones already handled in the literature. Additionally, we modify the Adams-type predictor-corrector method by implicitly implementing the Gauss–Seidel method in order to solve some specific particular cases of the system.http://dx.doi.org/10.1155/2021/3058414 |
| spellingShingle | Zaid Laadjal Qasem M. Al-Mdallal Fahd Jarad Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions Journal of Mathematics |
| title | Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions |
| title_full | Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions |
| title_fullStr | Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions |
| title_full_unstemmed | Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions |
| title_short | Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions |
| title_sort | analysis of a coupled system of nonlinear fractional langevin equations with certain nonlocal and nonseparated boundary conditions |
| url | http://dx.doi.org/10.1155/2021/3058414 |
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