Numerical Solutions of One-Dimensional Space Fractional Diffusion Equation Using Least-Squares Petrov-Galerkin Approach.

In this work, we proposed a novel method for solving onedimensional space fractional diffusion equations (SFDE) based on combining the least-squares method with PetrovGalerkin approach, utilizing orthogonal polynomials as basis functions, with the fractional derivative considered in the Caputo-Fabri...

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Publicado en:Journal of Basrah Researches (Sciences) Vol. 51; no. 2; pp. 75 - 88
Autores principales: Jumaa, Sara Qasim, Al-Humedi, Hameeda O.
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: Numerical Solutions of One-Dimensional Space Fractional Diffusion Equation Using Least-Squares Petrov-Galerkin Approach.
      aug:
        au:
          Jumaa, Sara Qasim
          Al-Humedi, Hameeda O.
        affil:
          General Directorate of Education in Missan, Ministry of Education, Iraq.
          Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq.
      su:
        Fractional differential equations
        Least squares
        MatLab (Computer software)
        Error analysis in mathematics
        Numerical solutions to equations
        Orthogonal polynomials
        Galerkin methods
        Fractional calculus
      sug:
        subj:
          Fractional differential equations
          Least squares
          MatLab (Computer software)
          Error analysis in mathematics
          Numerical solutions to equations
          Orthogonal polynomials
          Galerkin methods
          Fractional calculus
      keyword:
        Caputo-Fabrizio Fractional Derivative
        Chebyshev Polynomial
        Laguerre Polynomial
        Least-Squares Method
        One-Dimensional Space-Fractional Diffusion Equation
        Petrov-Galerkin Method
        طريقة المربعاتالصغرى
        طريقة بيتروف-جالر َكن
        متعددة الحدود شيبشيف، متعددة الحدودال َكوير
        مشتق كابوتو فابريزيو الكسري
        معادلة االنتشار الكسرية في ال فضاءأحادي البع
      ab: In this work, we proposed a novel method for solving onedimensional space fractional diffusion equations (SFDE) based on combining the least-squares method with PetrovGalerkin approach, utilizing orthogonal polynomials as basis functions, with the fractional derivative considered in the Caputo-Fabrizio sense. This method is to express the unknown function as a series of orthogonal polynomials that are linearly combined. By using this approach, we can turn the problem into a system of linear algebraic equations that can be solved using MATLAB R2023a for the unknown constants associated with the approximate solution. We provide two examples that illustrate the accuracy of our method and its ability to be applied effectively. The graphs and error tables support the proposed approach's effectiveness and efficiency. The results indicate that the proposed method yields more accurate solutions than others for solving similar problems.
      pubtype: Academic Journal
      doctype: Article
      src: R
    language: English
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