Vectorial Inverse Sturm-Liouville Problem With Local Derivative

Abstract

This study provides proof of the Ambarzumyan theorem for the n$$ n $$-dimensional vectorial Sturm-Liouville problem. In defining the problem, we applied local derivative which is conformable. Notably, we observed that the multiplicity of eigenvalues is n in this problem. Furthermore, we obtained identical results when the boundary conditions were periodic and antiperiodic. Despite the similarity between our method and that used in the classical problem, we believe that our results will contribute to the field of vectorial Sturm-Liouville problems.