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Lyapunov Inequality for a Fractional Differential Equation Modeling Damped Vibrations of Thin Film MEMS

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Abstract

We study a boundary value problem for a fractional differential equation modeling the damped vibrations of thin film MEMS with variable potential. The principal differential part of the equation under consideration is the composition of left- and right-sided Caputo derivatives. We find sufficient conditions for the potential which guarantee the uniqueness and solvability of the problem under study. The condition we give has an integral form and is an analog of the Lyapunov inequality.

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