Existence, uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ-Riemann-Liouville and ψ-Caputo fractional derivatives
Abstract This study delves into the existence, uniqueness, and stability of solutions for a nonlinear coupled system incorporating mixed generalized fractional derivatives. The system is characterized by ψ-Caputo and ϕ-Riemann-Liouville fractional derivatives with mixed boundary conditions. We provi...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-01994-z |
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| _version_ | 1832594545370464256 |
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| author | Said Zibar Brahim Tellab Abdelkader Amara Homan Emadifar Atul Kumar Sabir Widatalla |
| author_facet | Said Zibar Brahim Tellab Abdelkader Amara Homan Emadifar Atul Kumar Sabir Widatalla |
| author_sort | Said Zibar |
| collection | DOAJ |
| description | Abstract This study delves into the existence, uniqueness, and stability of solutions for a nonlinear coupled system incorporating mixed generalized fractional derivatives. The system is characterized by ψ-Caputo and ϕ-Riemann-Liouville fractional derivatives with mixed boundary conditions. We provide essential preliminaries and definitions, followed by a detailed analysis using fixed point theory to establish the main results. Furthermore, we discuss the Hyers-Ulam stability of the proposed system and illustrate the theoretical findings with several examples. This study extends and generalizes various results in the literature and provides new insights into the qualitative behavior of fractional differential systems. |
| format | Article |
| id | doaj-art-4f8f29926d9146538c7e9c269089eeab |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-4f8f29926d9146538c7e9c269089eeab2025-01-19T12:33:19ZengSpringerOpenBoundary Value Problems1687-27702025-01-012025112110.1186/s13661-025-01994-zExistence, uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ-Riemann-Liouville and ψ-Caputo fractional derivativesSaid Zibar0Brahim Tellab1Abdelkader Amara2Homan Emadifar3Atul Kumar4Sabir Widatalla5Applied Mathematics Laboratory, Kasdi Merbah UniversityApplied Mathematics Laboratory, Kasdi Merbah UniversityApplied Mathematics Laboratory, Kasdi Merbah UniversityDepartment of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha UniversityDepartment of Mathematics, Dayalbagh Educational InstituteDepartment of Mathematics, Faculty of Science, University of TabukAbstract This study delves into the existence, uniqueness, and stability of solutions for a nonlinear coupled system incorporating mixed generalized fractional derivatives. The system is characterized by ψ-Caputo and ϕ-Riemann-Liouville fractional derivatives with mixed boundary conditions. We provide essential preliminaries and definitions, followed by a detailed analysis using fixed point theory to establish the main results. Furthermore, we discuss the Hyers-Ulam stability of the proposed system and illustrate the theoretical findings with several examples. This study extends and generalizes various results in the literature and provides new insights into the qualitative behavior of fractional differential systems.https://doi.org/10.1186/s13661-025-01994-zFractional differential equationsFixed point theoryHyers-Ulam stabilityQualitative analysisψ-Caputo fractional derivativeϕ-Riemann-Liouville fractional derivative |
| spellingShingle | Said Zibar Brahim Tellab Abdelkader Amara Homan Emadifar Atul Kumar Sabir Widatalla Existence, uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ-Riemann-Liouville and ψ-Caputo fractional derivatives Boundary Value Problems Fractional differential equations Fixed point theory Hyers-Ulam stability Qualitative analysis ψ-Caputo fractional derivative ϕ-Riemann-Liouville fractional derivative |
| title | Existence, uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ-Riemann-Liouville and ψ-Caputo fractional derivatives |
| title_full | Existence, uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ-Riemann-Liouville and ψ-Caputo fractional derivatives |
| title_fullStr | Existence, uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ-Riemann-Liouville and ψ-Caputo fractional derivatives |
| title_full_unstemmed | Existence, uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ-Riemann-Liouville and ψ-Caputo fractional derivatives |
| title_short | Existence, uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ-Riemann-Liouville and ψ-Caputo fractional derivatives |
| title_sort | existence uniqueness and stability analysis of a nonlinear coupled system involving mixed ϕ riemann liouville and ψ caputo fractional derivatives |
| topic | Fractional differential equations Fixed point theory Hyers-Ulam stability Qualitative analysis ψ-Caputo fractional derivative ϕ-Riemann-Liouville fractional derivative |
| url | https://doi.org/10.1186/s13661-025-01994-z |
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