Adams-Bashforth Scheme and Kayo-Kengne-Akgül Derivative: Connexion and Chaotic Modelling
Universal Journal of Mathematics and Applications, cilt.9, sa.1, ss.53-63, 2026 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 9 Sayı: 1
- Basım Tarihi: 2026
- Doi Numarası: 10.32323/ujma.1879909
- Dergi Adı: Universal Journal of Mathematics and Applications
- Derginin Tarandığı İndeksler: Scopus, Applied Science & Technology Source, Central & Eastern European Academic Source (CEEAS), Directory of Open Access Journals
- Sayfa Sayıları: ss.53-63
- Anahtar Kelimeler: Advanced mathematical literacy, Complex systems modelling for sustainability, Computational tools for disaster resilience, Multi-disciplinary data analysis, Non-linear dynamics for global goals, Scientific research and innovation
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Karadeniz Teknik Üniversitesi Adresli: Evet
Özet
In this paper, we propose a novel formulation of the Adams–Bashforth scheme for solving fractional differential equations (FDEs) involving the Caputo-type Kayo–Kengne–Akgül derivative. We first recall the formal definitions of this derivative and its associated integral, establishing their existence and boundedness. By verifying the Fundamental Theorem of Calculus for this framework, we demonstrate that the integral is the exact inverse of the Caputo-type operator. We then extend the Adams–Bashforth scheme to FDEs by formulating the corresponding Cauchy problem and applying the inverse relationship. Following temporal discretization, the underlying functions are approximated using two-step Lagrange interpolation. By evaluating the resulting fractional integrals, we derive the explicit Adams–Bashforth iterative scheme. Furthermore, we provide a rigorous analysis of the truncation error, convergence, and stability of the proposed method. Finally, the effectiveness of the proposed numerical framework is demonstrated through its application to a three-dimensional chaotic flow system.