AccScience Publishing / IJOCTA / Online First / DOI: 10.36922/IJOCTA025320139
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RESEARCH ARTICLE

A rational power function-based approach for solving rational fractional differential equations

Babak Shiri1* ,  Aml Shloof2 ,  Norazak Senu3 ,  Dumitru Baleanu4
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1 Key Laboratory of Numerical Simulation of Sichuan Provincial Universities, College of Mathematics and Information Sciences, Neijiang Normal University, China
2 Department of Mathematics, Faculty of Science, University of Zintan, Libya
3 Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor, Malaysia
4 Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
IJOCTA 2026, 16(1), 370–382; https://doi.org/10.36922/IJOCTA025320139
Received: 4 August 2025 | Revised: 10 October 2025 | Accepted: 15 October 2025 | Published online: 26 January 2026
© 2026 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

A highly efficient and accurate numerical method for systems of fractional differential equations (FDEs) with rational order is presented in this paper. Rational power functions and rational Taylor series projection are utilized to obtain approximate solutions. Rational semi-smooth spaces are introduced, and the regularity of solutions in these spaces is established. A series of theoretical results, such as the existence and uniqueness of solutions, properties of the rational Taylor series and its remainder term, and an operational matrix approach, are derived. It is proven that the numerical solution is exact when the exact solution is a rational power series, and the approximate solution is shown to be the rational Taylor series projection of the exact solution. The convergence of the method is analyzed. The efficiency of the proposed method is demonstrated through numerical experiments, which show significant improvements in computational time compared to existing methods.

Keywords
Caputo derivative
Fractional differential equations
Rational power functions
Operational matrix
Rational Taylor series
Rational semi-smooth spaces
Funding
This research is supported by the Neijiang Normal University school-level science and technology project (key project, No. XJ2024008301).
Conflict of interest
The authors declare they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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