We establish various uniqueness results for inverse spectral problems of Sturm-Liouville operators with a finite number of discontinuities at interior points at which we impose the usual transmission conditions. We consider both the cases of classical Robin and of eigenparameter dependent boundary conditions. 2010 Mathematics Subject Classification. Primary 34B20, 34L05; Secondary 34B24, 47A10. Key words and phrases. Inverse Sturm-Liouville problem, eigenparameter dependent boundary conditions, internal discontinuities.

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In this paper, a novel fractional‐integer integral type sliding mode technique for control and generalized function projective synchronization of different fractional‐order chaotic systems with different dimensions in the presence of disturbances is presented. When the upper bounds of the disturbances are known, a sliding mode control rule is proposed to insure the existence of the sliding motion in finite time. Furthermore, an adaptive sliding mode control is designed when the upper bounds of the disturbances are unknown. The stability analysis of sliding mode surface is given using the Lyapunov stability theory. Finally, the results performed for synchronization of three‐dimensional fractional‐order chaotic Hindmarsh‐Rose (HR) neuron model and two‐dimensional fractional‐order chaotic FitzHugh‐Nagumo (FHN) neuron model.