On fractional eigenvalue problems approximating Steklov eigenvalues

This paper explores novel extensions of the classical Steklov eigenvalue problem within a nonlocal fractional framework. While our approach is inspired by the foundational methods presented in [ 11 ], the primary novelty of this work lies in the unprecedented combination of a fractional operator with a Kirchhoff-type function to determine a complete sequence of eigenvalues. By integrating these elements, we establish a nonlocal eigenvalue problem that not only captures the complex nonlocal dynamics of Kirchhoff equations but also recovers the classical Steklov problem through a rigorous limiting process.