A mathematical approach to ABC fractional modeling of the Klein–Gordon equation
Makaleler > Tam Makale · 2026
Yazarlar: Fouzia Chita, Souad Ayadi, Mohammed Boukedroun, Meltem Erden Ege, Özgür EGE, Mohammed Rabih, Independent Researcher, Izmir 35000, Turkey
AIMS Mathematics, Uluslararası, Wos, 2026, cilt 11, ss 24060-24089
DOI: 10.3934/math.2026970
Özet
This work investigated a fractional Klein–Gordon model formulated with the Atangana–Baleanu (AB) fractional derivative. The physical motivation for employing this fractional operator was discussed, emphasizing its ability to describe time-dependent processes with memory effects. The mathematical model was established, and the existence and uniqueness of its solution were examined using fixed-point theory. In addition, the Laplace multistage telescoping decomposition method (LMTDM) was introduced and applied to obtain approximate analytical solutions. The effectiveness of the proposed approach was evaluated through a comparison of absolute errors with those obtained using the Laplace Adomian decomposition method (LADM). The numerical results indicated that the LMTDM provides accurate approximations and exhibits good convergence properties, making it a reliable technique for solving fractional Klein–Gordon equations.