The objective of this paper is to solve the equation of motion of semilunar heart valve vibrations. The vibrations of the closed semilunar valves were modeled with a Caputo hactional derivative of order α. With the help of Laplace transformation, closed-form solution is obtained for the equation of motion in terms of Mittag-Leffler function. An alternative Method for Semi-differential equation, when α = 0.5, is examined using MATHEMATICA. The simplicity of these solutions makes them ideal for testing the accuracy of numerical methods. This solution can be of some interest for a better fit of experimental data.

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