In this article, we manifest the existence of a new class of \(\alpha \) -fractal functions without endpoint conditions in the space of continuous functions. Furthermore, we add the existence of the same class in numerous spaces such as the Hölder space, the convex Lipschitz space, and the oscillation space. We also estimate the fractal dimensions of the graphs of the newly constructed \(\alpha \) -fractal functions adopting some function spaces and covering methods.
