Fejér-Quadrature Collocation Algorithm for Solving Fractional Integro-Differential Equations via Fibonacci Polynomials

Authors

  • Y. H. Youssri Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt https://orcid.org/0000-0003-0403-8797
  • A. G. Atta Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt

DOI:

https://doi.org/10.37256/cm.5120244054

Keywords:

Fibonacci polynomials, Fejér quadrature, collocation method, fractional-order integro-differential equations

Abstract

In this article, we introduce a novel spectral algorithm utilizing Fibonacci polynomials to numerically solve both linear and nonlinear integro-differential equations with fractional-order derivatives. Our approach employs a quadrature-collocation method, transforming complex equations and associated conditions into systems of linear or nonlinear algebraic equations. The solutions to these equations, involving unknown coefficients, provide accurate numerical approximations for the original fractional-order equations. To validate the method, we present numerical examples illustrating its robustness and versatility. Comparative analyses with available analytical solutions affirm the reliability and accuracy of our algorithm, establishing its practical utility in addressing fractional-order integro-differential equations. This research contributes to computational mathematics and spectral methods, offering a promising tool for diverse scientific and engineering challenges.

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Published

2024-01-16

How to Cite

1.
Youssri YH, Atta AG. Fejér-Quadrature Collocation Algorithm for Solving Fractional Integro-Differential Equations via Fibonacci Polynomials. Contemp. Math. [Internet]. 2024 Jan. 16 [cited 2024 Jun. 17];5(1):296-308. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/4054