A Numerical Fractional Spline for Solving System of Fractional Differential Equations

Hamasalh, Faraidun Kadir; Hasan, Paywast Jabar

doi:10.32894/kujss.2025.162625.1228

	A Numerical Fractional Spline for Solving System of Fractional Differential Equations
Kirkuk Journal of Science
Volume 20, Issue 3, September 2025, Pages 20-30 PDF (304.86 K)
Document Type: Research Paper
DOI: 10.32894/kujss.2025.162625.1228
Authors
Faraidun Kadir Hamasalh^* ¹; Paywast Jabar Hasan²
¹Mathematics Department, Bakrajo Technical Institute, Sulaimani Polytechnic University, Sulaimani, iraq
²Mathematics 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.
Keywords
Boundary-value problem; Gamma function; Caputo fractional derivative; Riemann-Liouville fractional derivative; convergence analysis; errors estimation

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