Akbiyik, MucahitAlo, JetaAkbiyik, Seda Yamac2026-01-312026-01-3120252075-1680https://doi.org./10.3390/axioms14090665https://hdl.handle.net/20.500.12662/10812This study investigates curves in a 7-dimensional space, represented by spatial generalized octonion-valued functions of a single variable, where the general octonions include real, split, semi, split semi, quasi, split quasi, and para octonions. We begin by constructing a new frame, referred to as the G2-frame, for spatial generalized octonionic curves, and subsequently derive the corresponding derivative formulas. We also present the connection between the G2-frame and the standard orthonormal basis of spatial generalized octonions. Moreover, we verify that Frenet-Serret formulas hold for spatial generalized octonionic curves. We establish the G2-congruence of two spatial generalized octonionic curves and present the correspondence between the Frenet-Serret frame and the G2-frame. A key advantage of the G2-frame is that the associated frame equations involve lower-order derivatives. This method is both time-efficient and computationally efficient. To demonstrate the theory, we present an example of a unit-speed spatial generalized octonionic curve and compute its G2-frame and invariants using MATLAB.eninfo:eu-repo/semantics/openAccessgeneralized octonionscurvaturesFrenet-Serret frame formulaeArticle10.3390/axioms14090665914WOS:001579404500001Q2