A Numerical Fractional Spline for Solving System of Fractional Differential Equations

Document Type : Research Paper

Authors

1 Mathematics Department, Bakrajo Technical Institute, Sulaimani Polytechnic University, Sulaimani, iraq

2 Mathematics Department, College of Education, Sulaimani University, Sulaimani, Iraq

Abstract

Fractional-order differential equations are fundamental in diverse scientific and engineering fields, including population dynamics, optimal control, and physics. This paper presents a non-polynomial spline method for their numerical solution, establishing a linear system of algebraic equations in the representation of three-term recurrence equations, which is solved using an elimination algorithm. The maximum error estimations and the order of convergence for each example demonstrate the success and core contribution of the method and its performance is demonstrated through numerical and graphical examples. There is a thorough explanation of a mathematical procedure provided, as well as graphical and numerical examples for solving several examples. Results confirm that the proposed approach achieves superior accuracy and reliability compared to existing techniques.

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Kirkuk Journal of Science
Volume 20, Issue 3
September 2025
Page 20-30

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History

  • Receive Date: 09 July 2025
  • Revise Date: 19 August 2025
  • Accept Date: 19 August 2025

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