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.
MOLAEI, MOHAMMAD; SAEI, FARHAD DASTMALCHI; JAVIDI, MOHAMMAD; and MAHMOUDI, YAGHOUB
"Solving a class of ordinary differential equations and fractional differential equations with conformable derivative by fractional Laplace transform,"
Turkish Journal of Mathematics: Vol. 46:
7, Article 30.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss7/30