We consider a conformable 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?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.