Existence and stability of nonlinear discrete fractional initial value problems with application to vibrating eardrum.

It is well known that Newton's second law can be applied in various biological processes including the behavior of vibrating eardrums. In this work, we consider a nonlinear discrete fractional initial value problem as a model describing the dynamic of vibrating eardrum. We establish sufficient conditions for the existence, uniqueness, and Hyers-Ulam stability for the solutions of the proposed model.