Solving a class of ordinary differential equations and fractional differential equations with conformable derivative by fractional Laplace transform

Authors: MOHAMMAD MOLAEI, FARHAD DASTMALCHI SAEI, MOHAMMAD JAVIDI, YAGHOUB MAHMOUDI

Abstract: In this paper, we use the fractional Laplace transform to solve a class of second-order ordinary differential equations (ODEs), as well as some conformable fractional differential equations (CFDEs), including the Laguerre conformable fractional differential equation. Specifically, we apply the transform to convert the differential equations into first-order, linear differential equations. This is done by using the fractional Laplace transform of order $\alpha+\beta$ or $\alpha+\beta+\gamma$. Also, we investigate some more results on the fractional Laplace transform, obtained by Abdeljawad.

Keywords: Fractional Laplace transform, conformable fractional derivative, conformable fractional differential equation, Laguerre conformable fractional differential equation

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