Inverse nodal problem for Fractional Sturm-Liouville operator with Jump Conditions

Abstract

We consider a fractional Sturm-Liouville problem with the discontinuous(or jump) condition inside the interval. The asymptotic formulas for the eigenvalues, nodal parameters (nodal points and nodal lengths) of this problem are calculated by the modified Pr\"{u}fer substitutions. Also, using these asymptotic formulas, an explicit formula for the potential functions is given. After all, we discuss Lipschitz stability for the considered problem.We consider a fractional Sturm-Liouville problem with the discontinuous(or jump) condition inside the interval. The asymptotic formulas for the eigenvalues, nodal parameters (nodal points and nodal lengths) of this problem are calculated by the modified Pr\"{u}fer substitutions. Also, using these asymptotic formulas, an explicit formula for the potential functions is given. After all, we discuss Lipschitz stability for the considered problem.