Fractional Sturm–Liouville problem on metric graphs

In the talk, we will explore the fractional analog of the Sturm-Liouville problem on a metric graph using a combination of left Riemann-Liouville and right Caputo fractional derivatives. This combination creates a symmetric and positive analog of the Sturm-Liouville operator. We demonstrated that the operator has a countable number of eigenvalues converging to infinity. Furthermore, we analyzed the convergence of the series $\sum\limits_{k=1}^{\infty }{\frac{1}{{{\lambda }_{k}}}}$ and provide estimates for the eigenfunctions.