A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling waves
In this work, we begin by introducing a new notion of coupled closed fractional boundary conditions to study a class of nonlinear sequential systems of Caputo fractional differential equations. The existence and uniqueness of solutions for the class of systems is proved by applying Banach contracti...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2025-04-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://bmee.vgtu.lt/index.php/MMA/article/view/20920 |
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| author | Abdelkader Lamamri Yazid Gouari Zoubir Dahmani Mahdi Rakah Mehmet Zeki Sarıkaya |
| author_facet | Abdelkader Lamamri Yazid Gouari Zoubir Dahmani Mahdi Rakah Mehmet Zeki Sarıkaya |
| author_sort | Abdelkader Lamamri |
| collection | DOAJ |
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In this work, we begin by introducing a new notion of coupled closed fractional boundary conditions to study a class of nonlinear sequential systems of Caputo fractional differential equations. The existence and uniqueness of solutions for the class of systems is proved by applying Banach contraction principle. The existence of at least one solution is then accomplished by applying Schauder fixed point theorem. The Ulam Hyers stability, with a limiting-case example, is also discussed. In a second part of our work, we use the tanh method to obtain a new travelling wave solution for the coupled system of Burgers using time and space Khalil derivatives. By bridging these two aspects, we aim to present an understanding of the system’s behaviour.
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| format | Article |
| id | doaj-art-c03e6ec58ee643de990058991ad0ef58 |
| institution | DOAJ |
| issn | 1392-6292 1648-3510 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj-art-c03e6ec58ee643de990058991ad0ef582025-08-20T03:18:52ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102025-04-0130210.3846/mma.2025.20920A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling wavesAbdelkader Lamamri0Yazid Gouari1Zoubir Dahmani2Mahdi Rakah3Mehmet Zeki Sarıkaya4LAMDA-RO Laboratory, Department of Mathematics, University of Blida 1, Blida, Algeria27000 Ecole Normale de Mostaganem, Mostaganem, AlgeriaLAMDA-RO Laboratory, Department of Mathematics, University of Blida 1, Blida, AlgeriaUniversity of Alger 1, Alger, AlgeriaDepartment of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Türkiye In this work, we begin by introducing a new notion of coupled closed fractional boundary conditions to study a class of nonlinear sequential systems of Caputo fractional differential equations. The existence and uniqueness of solutions for the class of systems is proved by applying Banach contraction principle. The existence of at least one solution is then accomplished by applying Schauder fixed point theorem. The Ulam Hyers stability, with a limiting-case example, is also discussed. In a second part of our work, we use the tanh method to obtain a new travelling wave solution for the coupled system of Burgers using time and space Khalil derivatives. By bridging these two aspects, we aim to present an understanding of the system’s behaviour. https://bmee.vgtu.lt/index.php/MMA/article/view/20920Caputo sequential derivativecoupled system of FDEsexistence and uniquenessUlam-Hyers stabilityfixed point theoremtravelling wave |
| spellingShingle | Abdelkader Lamamri Yazid Gouari Zoubir Dahmani Mahdi Rakah Mehmet Zeki Sarıkaya A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling waves Mathematical Modelling and Analysis Caputo sequential derivative coupled system of FDEs existence and uniqueness Ulam-Hyers stability fixed point theorem travelling wave |
| title | A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling waves |
| title_full | A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling waves |
| title_fullStr | A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling waves |
| title_full_unstemmed | A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling waves |
| title_short | A class of nonlinear systems with new boundary conditions: existence of solutions, stability and travelling waves |
| title_sort | class of nonlinear systems with new boundary conditions existence of solutions stability and travelling waves |
| topic | Caputo sequential derivative coupled system of FDEs existence and uniqueness Ulam-Hyers stability fixed point theorem travelling wave |
| url | https://bmee.vgtu.lt/index.php/MMA/article/view/20920 |
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