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

Math Biosci Eng. 2021 May 6;18(4):3907-3921. doi: 10.3934/mbe.2021195.


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. To examine the validity of our findings, a concrete example of forced eardrum equation along with numerical simulation is analyzed.

Keywords: Hyers–Ulam stability; existence and uniqueness; nonlinear discrete fractional problem; vibrating eardrum.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Computer Simulation
  • Tympanic Membrane*