A Novel Computational Technique for Numerical Approximation of Nonlinear Fractional Dynamical Systems: Convergence and Efficiency Analysis
Journal of Function Spaces, cilt.2026, sa.1, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 2026 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.1155/jofs/8234778
- Dergi Adı: Journal of Function Spaces
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Directory of Open Access Journals, Academic Search Ultimate (EBSCO), Middle East & Africa Database (ProQuest), Natural Science Collection (ProQuest), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: 34A08, 35R11, 65J15, 65M70, ABC derivative, convergence analysis, fractional derivatives, nonlinear fractional dynamical systems, numerical approximation, PSIM, stability
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
In this work, we study a family of nonlinear fractional dynamical systems and propose a numerical procedure based on the power series iterative method (PSIM). The systems are formulated in terms of the Atangana–Baleanu–Caputo (ABC) fractional derivative, which is well-suited to the modeling of memory and nonlocal effects. The method rewrites the original fractional system in an equivalent integral form and then constructs the solution through a simple iterative process, thereby yielding approximate solutions in a direct and systematic manner. We also investigate the main analytical properties of the method. In particular, we show that the PSIM sequence converges to the exact solution under suitable assumptions, and we establish stability results showing that small perturbations in the system produce only small variations in the corresponding solution. As an application, the method is implemented for the fractional Whitham–Broer–Kaup system (WBKS). The obtained results indicate that PSIM provides accurate approximations with rapid convergence, confirming that it is an effective and reliable tool for nonlinear fractional dynamical systems.