Existence and stability of nonlinear discrete fractional initial value problems with application to vibrating eardrum
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Updated: Oct 31, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
George Maria Selvam1, Jehad Alzabut2,3, Vignesh Dhakshinamoorthy1
1Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635601, Tamil Nadu, India.
Abstract:
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.
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