Ambarzumyan theorem for the N-dimensional comformabledifferentiable Sturm Liouville problem

In this study, we defined the matrix-valued Sturm-Liouville problem by a fractional derivative, which is referred to as a conformable derivative in the literature. In this problem, we have defined the potential function 𝑄(𝑥) as a symmetric matrix value type 𝑁 × 𝑁. We gave the Ambarzumyan theorem and the proof of this theorem for such a problem. We also showed that for periodic and anti-periodic problems, each element of the potential matrix function can be found with by the first eigenvalue of the problem. Finally, we examined the spectral data for a two-dimensional problem. As a result, we saw that in the conformable differentional problem, the multiplicity of the eigenvalues is the same as the dimension of the problem