ON THE STABILITY OF A DEGENERATE AND SINGULAR VIBRATING EQUATION UNDER FRACTIONAL DERIVATIVE CONTROLS

Abstract

In this paper, we consider one-dimentional of degenerate and singular wave equations
with the fractional feedback acting on one end only. First, we reformulate each system
into an augmented model and using a general criteria of Arendt-Batty, we prove that our
models are strongly stable. Next, by using a spectrum method, we establish nonuniform
stabilization. Using a frequency domain approach we prove some polynomial energy decay
rate depending on the order of the fractional derivative.