Finite Difference Approximation with the Quadrature Method for Solving Fredholm IntegroDifferential Equations of Fractional Order.
In this article, effective techniques are described to solve numerically the Fredholm integro-differential equations of multi-fractional order that lie in (0,1] in the Caputo sense (FIFDEs). The approach uses finite difference approximation to Caputo derivative utilizing collocation points and is ba...
| Publicado en: | Journal of Basrah Researches (Sciences) Vol. 51; no. 2; pp. 1 - 22 |
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| Autores principales: | , |
| Formato: | Artículo |
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Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR)
2025
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=191821451&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 191821451 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 18172695 GYGY jtl: Journal of Basrah Researches (Sciences) issn: 18172695 maglogo: N pubinfo: dt: 2025 vid: 51 iid: 2 pid: 25427 pub: Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) artinfo: ui: 191821451 10.56714/bjrs.51.2.1 ppf: 1 ppct: 21 formats: tig: atl: Finite Difference Approximation with the Quadrature Method for Solving Fredholm IntegroDifferential Equations of Fractional Order. aug: au: Zahir, Dashne Chapuk Ahmed, Shazad Shawki affil: Department of Mathematics, Faculty of Science and Health, Koya University, Koya 46017, Iraq. Department of Mathematics, College of Science, Sulaimani University, Sulaymaniyah 46001, Iraq. su: Finite difference method Caputo fractional derivatives Numerical integration Numerical analysis Fredholm equations Fractional calculus sug: subj: Finite difference method Caputo fractional derivatives Numerical integration Numerical analysis Fredholm equations Fractional calculus keyword: CaputoFractional Derivative Forward Difference Approximation Fractional Calculus IntegralDifferential Equation Newton-Cotes Quadrature Technique Simpson’s Method Trapezoidal Method المشتقة الكسرية كابوتو المعادلة التكاملية التفاضلية تقريب الفرق الأمامي تقنية تربيع نيوتن كوت حساب الكسور طريقة سيمبسون طريقة شبه المنحرف ab: In this article, effective techniques are described to solve numerically the Fredholm integro-differential equations of multi-fractional order that lie in (0,1] in the Caputo sense (FIFDEs). The approach uses finite difference approximation to Caputo derivative utilizing collocation points and is based on the quadrature rule, Trapezoidal, and Simpson process. 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 trapezoidal and Simpson rules, to create a finite difference formula for our fractional equation. Additionally, numerical examples are provided to demonstrate the validity and use of the approach as well as comparisons with earlier findings. The aforementioned procedure has been used to construct algorithms for treating FIFDEs. A MATLAB program is created to express these solutions. Furthermore, some numerical tests are provided to demonstrate the method's accuracy. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2025 holdings: @attributes: islocal: N |
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