A Fractional Calculus Model of Semilunar Heart Valve Vibrations

The objective of this paper is to solve the equation of motion of semilunar heart valve vibrations. The vibration of the closed semilunar valves are modeled by a Caputo fractional derivative of order α. Using a Laplace transformation, a closed-form solution is obtained for the equation of motion in terms of a Mittag-Leffler function. An alternative method for a semi-differential equation α = 1/2 when is also examined. The simplicity of the Mathematica solution makes it ideal for testing the accuracy of numerical methods. This solution can be of some interest for fitting experimental data.