Analyzing the stability of coupled nonlinear fractional Volterra–Fredholm integro-differential equations with a modern method for numerical solutions
Abstract In this study, we examine the coupled nonlinear fractional Volterra–Fredholm integro-differential equations that utilize Caputo fractional derivatives. The primary objective of this research is to explore the existence, uniqueness, stability of solutions, and convergence analysis using the...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02031-9 |
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| author | Maryam Mohseni Davood Rostamy |
| author_facet | Maryam Mohseni Davood Rostamy |
| author_sort | Maryam Mohseni |
| collection | DOAJ |
| description | Abstract In this study, we examine the coupled nonlinear fractional Volterra–Fredholm integro-differential equations that utilize Caputo fractional derivatives. The primary objective of this research is to explore the existence, uniqueness, stability of solutions, and convergence analysis using the fractional-order biorthogonal flatlet multiwavelet collocation method (FBFMCM) for the specified coupled integro-differential equations. We begin by demonstrating the existence and uniqueness of the solution to the problem through the application of the well-established Krasnoselskii theorem and the Banach contraction principle. Next, we analyze the Ulam–Hyers and Ulam–Hyers–Rassias stability for the problem at hand. Finally, we present the implementation of the proposed method along with a convergence analysis. Additionally, we compute the operational matrix for fractional integration and provide an example to illustrate our main findings. |
| format | Article |
| id | doaj-art-0c8a0ff01e16406c99d5d0d1cebc8971 |
| institution | OA Journals |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-0c8a0ff01e16406c99d5d0d1cebc89712025-08-20T02:10:50ZengSpringerOpenBoundary Value Problems1687-27702025-05-012025113410.1186/s13661-025-02031-9Analyzing the stability of coupled nonlinear fractional Volterra–Fredholm integro-differential equations with a modern method for numerical solutionsMaryam Mohseni0Davood Rostamy1Department of Applied Mathematics, Imam Khomeini International UniversityDepartment of Applied Mathematics, Imam Khomeini International UniversityAbstract In this study, we examine the coupled nonlinear fractional Volterra–Fredholm integro-differential equations that utilize Caputo fractional derivatives. The primary objective of this research is to explore the existence, uniqueness, stability of solutions, and convergence analysis using the fractional-order biorthogonal flatlet multiwavelet collocation method (FBFMCM) for the specified coupled integro-differential equations. We begin by demonstrating the existence and uniqueness of the solution to the problem through the application of the well-established Krasnoselskii theorem and the Banach contraction principle. Next, we analyze the Ulam–Hyers and Ulam–Hyers–Rassias stability for the problem at hand. Finally, we present the implementation of the proposed method along with a convergence analysis. Additionally, we compute the operational matrix for fractional integration and provide an example to illustrate our main findings.https://doi.org/10.1186/s13661-025-02031-9Existence-uniqueness resultFractional VolterraFredholm integro-differential equationFractional-order biorthogonal flatlet multiwaveletOperational matrixUlam stability |
| spellingShingle | Maryam Mohseni Davood Rostamy Analyzing the stability of coupled nonlinear fractional Volterra–Fredholm integro-differential equations with a modern method for numerical solutions Boundary Value Problems Existence-uniqueness result Fractional Volterra Fredholm integro-differential equation Fractional-order biorthogonal flatlet multiwavelet Operational matrix Ulam stability |
| title | Analyzing the stability of coupled nonlinear fractional Volterra–Fredholm integro-differential equations with a modern method for numerical solutions |
| title_full | Analyzing the stability of coupled nonlinear fractional Volterra–Fredholm integro-differential equations with a modern method for numerical solutions |
| title_fullStr | Analyzing the stability of coupled nonlinear fractional Volterra–Fredholm integro-differential equations with a modern method for numerical solutions |
| title_full_unstemmed | Analyzing the stability of coupled nonlinear fractional Volterra–Fredholm integro-differential equations with a modern method for numerical solutions |
| title_short | Analyzing the stability of coupled nonlinear fractional Volterra–Fredholm integro-differential equations with a modern method for numerical solutions |
| title_sort | analyzing the stability of coupled nonlinear fractional volterra fredholm integro differential equations with a modern method for numerical solutions |
| topic | Existence-uniqueness result Fractional Volterra Fredholm integro-differential equation Fractional-order biorthogonal flatlet multiwavelet Operational matrix Ulam stability |
| url | https://doi.org/10.1186/s13661-025-02031-9 |
| work_keys_str_mv | AT maryammohseni analyzingthestabilityofcouplednonlinearfractionalvolterrafredholmintegrodifferentialequationswithamodernmethodfornumericalsolutions AT davoodrostamy analyzingthestabilityofcouplednonlinearfractionalvolterrafredholmintegrodifferentialequationswithamodernmethodfornumericalsolutions |