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

DOI

10.55730/1300-0098.3316

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

First Page

3025

Last Page

3044

Recommended Citation

MOLAEI, MOHAMMAD; SAEI, FARHAD DASTMALCHI; JAVIDI, MOHAMMAD; and MAHMOUDI, YAGHOUB (2022) "Solving a class of ordinary differential equations and fractional differential equations with conformable derivative by fractional Laplace transform," Turkish Journal of Mathematics: Vol. 46: No. 7, Article 30. https://doi.org/10.55730/1300-0098.3316
Available at: https://journals.tubitak.gov.tr/math/vol46/iss7/30