Cubic B-Spline Finite Element Method for Fractional Ordinary Differential Equations

Document Type : Original Article

Authors
Bashdar Omer Hussen 1
Younis A. Sabawi 2
Mardan Ameen Pirdawood 3
1 1Department of Computer Science, Faculty of Science and Health, Koya University, Koya 46017, Kurdistan Region, Iraq.
2 Department of Mathematics, Faculty of Science and Health, Koya University, Koya 46017, Kurdistan Region, Iraq.
3 College of Information Technology, Imam Ja’afar AL-Sadiq University, Baghdad, Iraq.
10.24271/psr.2025.516965.2076
Abstract
The paper offers a numerical approximation for fractional ordinary differential equations in which the first and second-order are replaced by a fractional derivative. We have employed the cubic B-spline approach coupled with the finite element approach to sort out such problems. Also discussed exploring fractional differential equations by proving the existence and uniqueness of their solutions, along with the correctness of their error estimations. The error estimation is derived by the Aubin–Nitsche duality argument. The efficiency of all the proposed approaches is compared in several numerical examples in order to verify, demonstrate and display the applicability of the approach, as well as to compare the estimated outcomes with analytical result.
Keywords
Aubin&ndash
Nitsch duality argument, Convergence analysis, Caputo method, Finite element method, fractional problems
Crossmark
Subjects
Passer Journal of Basic and Applied Sciences
Volume 8, Issue 1
January 2026
Pages 352-363