In this manuscript, we present a simple and efficient computational algorithm for solving eigenvalue problems of fractional second-order differential operators with a constant delay inside the interval. By transforming the the governing fractional differential equations with a constant delay into a linear system of algebraic equations, we can obtain the corresponding polynomial characteristic equations for kinds of boundary conditions based on the polynomial expansion and integral technique. Then, the eigenvalues can be calculated by finding the roots of the corresponding characteristic polynomial. The numerical results demonstrate reliability and efficiency of the proposed algorithm.
