A Midpoint Quadratic Approach for Solving Numerically Multi-Order Fractional Integro-Differential Equation
Background: This article presents a method for finding numerical solutions to Fredholm integro-differential equations (FIFDEs) with multi-fractional orders of one or less, using a useful algorithm. Materials and Methods: A finite difference approximation to Caputo's derivative using collocatio...
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| Veröffentlicht in: | Majallat Jāmiʻat Bābil S. 83 - 106 |
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| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
14.10.2025
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| ISSN: | 1992-0652, 2312-8135 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Background: This article presents a method for finding numerical solutions to Fredholm integro-differential equations (FIFDEs) with multi-fractional orders of one or less, using a useful algorithm. Materials and Methods: A finite difference approximation to Caputo's derivative using collocation points is used to build the midpoint method for the quadrature rule, which forms the basis of the approach. Results: Our method simplifies the evaluation of treatments by transforming the FIFDEs into algebraic equations with operational matrices. After calculating the Caputo derivative at a specific point using the finite difference method, we use the quadrature method, which includes the midpoint rule, to create a finite difference formula for our fractional equation. Conclusions: Additionally, numerical examples are provided to demonstrate the validity and use of the approach as well as comparisons with earlier findings. The results are expressed using a program created in MATLAB. |
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| ISSN: | 1992-0652 2312-8135 |
| DOI: | 10.29196/jubpas.v33i3.5974 |