Existence and stability of nonlinear discrete fractional initial value problems with application to vibrating eardrum
A. George Maria Selvam, Jehad Alzabut, D. Vignesh, Jagan Mohan Jonnalagadda, Kamaleldin Abodayeh
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.
Topics & Concepts
EardrumUniquenessNonlinear systemStability (learning theory)Work (physics)MathematicsMathematical analysisApplied mathematicsInitial value problemControl theory (sociology)Computer sciencePhysicsAcousticsQuantum mechanicsMachine learningArtificial intelligenceControl (management)ThermodynamicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisFunctional Equations Stability Results