Solving Systems of Fractional-Order Differential Equations Using a Reproducing Kernel-Based Approach

Taher Amoozad, Saeid Abbasbandy, Hussein Sahihi and Tofigh Allahviranloo

Journal of Mathematics, 2026, vol. 2026, 1-29

Abstract: This paper introduces a new technique utilizing the reproducing kernel method (RKM) to solve both linear and nonlinear systems of fractional-order differential equations (SFDEs). The technique carefully integrates essential elements, including the solution space, basis functions, strategic point selection, and a suitable inner product. While solving SFDEs can be notoriously complex, leading to issues such as extended computation times, elevated matrix condition numbers, reduced accuracy compared to alternative methods, and discrepancies between theoretical predictions and numerical outcomes, our approach effectively mitigates these challenges. We achieve this by eliminating the need for Gram–Schmidt orthogonalization and incorporating efficient linear algebra techniques. By strategically selecting the solution space and evaluation points, we develop an RKM-based approach that combines computational efficiency, high accuracy, and straightforward implementation.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2026/6967323.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2026/6967323.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6967323

DOI: 10.1155/jom/6967323

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().