Ulam Stability, Lyapunov-Type Inequality, and the Eigenvalue Problem for Model of Discrete Fractional-Order Deflection Equations of Vertical Columns and a Rotating String with Two-Point Boundary Conditions

Due to its significance in numerous scientific and engineering domains, discrete fractional calculus (DFC) has received much attention recently. In particular, it seems that the exploration of the stability of DFC is crucial. A mathematical model of the discrete fractional equation describing the deflection of a vertical column along with two-point boundary conditions featuring the Riemann–Liouville operator is constructed to study several kinds of Ulam stability results in this research work. In addition, we developed Lyapunov-type inequality and its application to an eigenvalue problem for discrete fractional rotating string equations. Finally, the effectiveness of the theoretical findings is demonstrated with numerical examples.