Abstract—Recently exact fractional differential equations have been introduced, using the conformable fractional derivative. In this paper, we propose and prove some new results on the integrating factor. We introduce a conformable version of several classical special cases for which the integrating factor can be determined. Specifically, the cases we will consider are where there is an integrating factor that is a function of only x, or a function of only y, or a simple formula of x and y. In addition, using the Conformable Euler's Theorem on homogeneous functions, an integration factor for the conformable homogeneous differential equations is established. Finally, the above results apply in some interesting examples.

Index Terms—A conformable Euler´s theorem, conformable fractional derivative, exact fractional differential equation, integrating factor.

F. Martínez, I. Martínez, S. Paredes are with Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, España.

Cite:F. Martínez, I. Martínez, S. Paredes, "A Note on Integrating Factors of a Conformable Fractional Differential Equation," International Journal of Applied Physics and Mathematics vol. 10, no. 4, pp. 143-152, 2020.

Copyright © 2020 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).