Fractional B-spline collocation method for the numerical solution of the fractional pantograph differential equations
Abstract A numerical method based on fractional B-spline is developed and examined to approximate the solution of fractional multiterm pantograph equations. The method is applied to a uniform partition, and the midpoints of the partition are used as extra points to construct a uniquely solvable syst...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-02-01
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| Series: | Boundary Value Problems |
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| Online Access: | https://doi.org/10.1186/s13661-025-02009-7 |
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| author | S. Bivani M. Ghasemi A. Goligerdian |
| author_facet | S. Bivani M. Ghasemi A. Goligerdian |
| author_sort | S. Bivani |
| collection | DOAJ |
| description | Abstract A numerical method based on fractional B-spline is developed and examined to approximate the solution of fractional multiterm pantograph equations. The method is applied to a uniform partition, and the midpoints of the partition are used as extra points to construct a uniquely solvable system. Convergence analysis of the method is discussed via Green’s function approach, and an error bound dependent on the regularity of the exact solution is obtained. Additionally, to demonstrate the efficiency and accuracy of the proposed method, several examples are solved. The results indicate that the practical orders of convergence obtained by our proposed method are in good agreement with the theoretical results. |
| format | Article |
| id | doaj-art-befcc0a619b140528a58e6374c336145 |
| institution | Kabale University |
| issn | 1687-2770 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj-art-befcc0a619b140528a58e6374c3361452025-02-09T12:47:44ZengSpringerOpenBoundary Value Problems1687-27702025-02-012025111910.1186/s13661-025-02009-7Fractional B-spline collocation method for the numerical solution of the fractional pantograph differential equationsS. Bivani0M. Ghasemi1A. Goligerdian2Department of Applied Mathematics, University of KurdistanDepartment of Applied Mathematics, University of KurdistanDepartment of Mathematics, University of HoustonAbstract A numerical method based on fractional B-spline is developed and examined to approximate the solution of fractional multiterm pantograph equations. The method is applied to a uniform partition, and the midpoints of the partition are used as extra points to construct a uniquely solvable system. Convergence analysis of the method is discussed via Green’s function approach, and an error bound dependent on the regularity of the exact solution is obtained. Additionally, to demonstrate the efficiency and accuracy of the proposed method, several examples are solved. The results indicate that the practical orders of convergence obtained by our proposed method are in good agreement with the theoretical results.https://doi.org/10.1186/s13661-025-02009-7Fractional pantograph equationsFractional B-splineGreen’s functionOrder of convergence |
| spellingShingle | S. Bivani M. Ghasemi A. Goligerdian Fractional B-spline collocation method for the numerical solution of the fractional pantograph differential equations Boundary Value Problems Fractional pantograph equations Fractional B-spline Green’s function Order of convergence |
| title | Fractional B-spline collocation method for the numerical solution of the fractional pantograph differential equations |
| title_full | Fractional B-spline collocation method for the numerical solution of the fractional pantograph differential equations |
| title_fullStr | Fractional B-spline collocation method for the numerical solution of the fractional pantograph differential equations |
| title_full_unstemmed | Fractional B-spline collocation method for the numerical solution of the fractional pantograph differential equations |
| title_short | Fractional B-spline collocation method for the numerical solution of the fractional pantograph differential equations |
| title_sort | fractional b spline collocation method for the numerical solution of the fractional pantograph differential equations |
| topic | Fractional pantograph equations Fractional B-spline Green’s function Order of convergence |
| url | https://doi.org/10.1186/s13661-025-02009-7 |
| work_keys_str_mv | AT sbivani fractionalbsplinecollocationmethodforthenumericalsolutionofthefractionalpantographdifferentialequations AT mghasemi fractionalbsplinecollocationmethodforthenumericalsolutionofthefractionalpantographdifferentialequations AT agoligerdian fractionalbsplinecollocationmethodforthenumericalsolutionofthefractionalpantographdifferentialequations |