Discrete WRM using Tau and Galerkin Techniques to Solve Multi-Higher Fractional Order Integro-Differential Equations of the Fredholm type

Authors

  • Dashne Chapuk Zahir Zahir 1Department of Mathematics, Faculty of Science and Health, Koya University, Koya 44023, Kurdistan Region-F.R. Iraq
  • Shazad Shawki Ahmed Department of Mathematics, College of Science, Sulaimani University, Sulaymaniyah 46001, Kurdistan Region, Iraq
  • Shabaz Jalil Mohammedfaeq Department of Mathematics, College of Science, Sulaimani University, Sulaymaniyah 46001, Kurdistan Region, Iraq
  • Hiwa Abdullah Rasol University of Raparin, College of Basic Education, Raniyah 46012, Iraq

DOI:

https://doi.org/10.56714/bjrs.51.2.12

Keywords:

Fractional order, Integro-differential equation, Fredholm type, Caputo derivative, Legendre polynomials, Chebyshev polynomials, Tau and Galerkin methods, Clenshaw-Curti's formula

Abstract

The goal of this article is to create and implement novel approaches for utilizing shifted Legendre and Chebyshev polynomials to solve multi-fractional order Fredholm integro-differential equations (FIDEs). The Tau and Galerkin methods will be used in conjunction with the discrete weighted residual approach. The Clenshaw-Curtis quadrature formula will be employed computationally to evaluate the integral terms. In order to identify orthogonal coefficients for approximate solutions, this study uses an operational matrix to transform FIDEs of the fractional orders into a system of linear algebraic equations. In order to obtain approximate solutions for the equation, this procedure enables the development of algorithms for each method. Additionally, the technique's validity, applicability, and similarities with previous results are illustrated and contrasted using numerical examples. Most applications are run on a computer with MATLAB V.9.7 installed

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Published

31-12-2025

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Vol. 51 No. 2 (2025)

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How to Cite

Discrete WRM using Tau and Galerkin Techniques to Solve Multi-Higher Fractional Order Integro-Differential Equations of the Fredholm type. (2025). Basrah Researches Sciences, 51(2), 29. https://doi.org/10.56714/bjrs.51.2.12

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