Numerical Solutions of One-Dimensional Space Fractional Diffusion Equation Using Least-Squares Petrov-Galerkin Approach. - Jumaa, Sara Qasim; Al-Humedi, Hameeda O. (Journal of Basrah Researches (Sciences), 2025)
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.