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In this work, we investigate a linear differential equation involvingCaputo-Fabrizio fractional derivative of order $1<\beta\leq 2$. Under someassumptions the considered equation is reduced to an integer order differentialequation and solutions for different cases are obtained in explicit forms. Wealso prove a uniqueness of a solution of an initial value problem with anonlinear differential equation containing the Caputo-Fabrizio derivative.Application of our result to the mass-spring-damper motion is also presented.

On a differential equation with Caputo-Fabrizio fractional derivative of order $1<\beta\leq 2$ and application to mass-spring-damper system