Remarks on the Solution of Fractional Ordinary Differential Equations Using Laplace Transform Method

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In this work we used the Laplace transform method to solve linear fractional-order differential equation, fractional ordinary differential equations with constant and variable coefficients. The solutions were expressed in terms of Mittag-Leffler functions, and then written in a compact simplified form. As a special case for simplicity, the order of the derivative determined the order of the solution that was obtained. This paper presented several case studies involving the implementation of Fractional Order calculus-based models, whose results demonstrate the importance of Fractional Order Calculus.