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...

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Publicado en:Journal of Basrah Researches (Sciences) Vol. 51; no. 2; pp. 1 - 22
Autores principales: Zahir, Dashne Chapuk, Ahmed, Shazad Shawki
Formato: Artículo
Publicado: Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) 2025
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Acceso en línea:Ver este registro en EBSCOhost
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        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
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