Advancing differential equation solutions: A novel Laplace-reproducing kernel Hilbert space method for nonlinear fractional Riccati equations

Ali Akgül and Nourhane Attia
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Ali Akgül: Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon2Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey
Nourhane Attia: National High School for Marine Sciences and Coastal (ENSSMAL), Dely Ibrahim University Campus, Bois des Cars, B.P. 19, 16320, Algiers, Algeria

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 02, 1-28

Abstract: Fractional ordinary differential equations are crucial for modeling various phenomena in engineering and physics. This study aims to enhance solution methodologies by combining the Laplace transform with the reproducing kernel Hilbert space method (RKHSM). This integration leads to a more effective approach compared to the classical RKHSM. We apply the Laplace-reproducing kernel Hilbert space method (L-RKHSM) to develop novel numerical solutions for nonlinear fractional Riccati differential equations. The L-RKHSM systematically produces both approximate and analytic solutions in series form. We present detailed results for four illustrative examples, showcasing the superior performance of the L-RKHSM over traditional methods. This innovative approach not only advances our understanding of nonlinear fractional ordinary differential equations but also demonstrates its effectiveness through significantly improved outcomes in various applications.

Keywords: Nonlinear fractional ordinary differential equations; Laplace transformation; reproducing kernel method; numerical solution (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183124501869

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