This paper presents a generalized finite element formulation for the analysis of truss and frame structures within the framework of space-fractional continuum mechanics. The approach incorporates non-local effects through the use of fractional-order derivatives, enabling the modeling of scale-sensitive behavior observed in micro- and nano-sized structures. A novel space-fractional finite element method is developed, supporting arbitrary structural topology and spatially varying length scale function. Special attention is given to the numerical convergence of the method, which depends on the fractional order, length scale function, and the number of interpolation nodes. The method ensures smooth convergence to classical solutions in the limit of integer-order derivatives and/or zero length scale. In addition to axial behavior in trusses, the extension to frame structures allows for the inclusion of bending and rotational effects in the fractional formulation. The presented examples confirm the numerical efficiency and stable convergence of the proposed method. ACKNOWLEDGEMENTS This research was funded in whole by the National Science Centre, Poland, grant number 2022/45/N/ST8/02421. For the purpose of Open Access, the authors have applied a CC-BY public copyright license to any Author Accepted Manuscript (AAM) version arising from this submission.