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

Document Type : Research Paper

Authors

Faraidun Kadir Hamasalh ¹

Paywast Jabar Hasan ²

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

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

10.32894/kujss.2025.162625.1228

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

Subjects