Open AccessA Note on Integrating Factors of a Conformable Fractional Differential Equation
Author(s) -
Francisco Martínez
Publication year - 2020
Publication title -
international journal of applied physics and mathematics
Language(s) - English
Resource type - Journals
ISSN - 2010-362X
DOI - 10.17706/ijapm.2020.10.4.143-152
Subject(s) - conformable matrix , homogeneous , euler's formula , mathematics , function (biology) , homogeneous differential equation , differential equation , differential (mechanical device) , mathematical analysis , fractional calculus , physics , ordinary differential equation , combinatorics , differential algebraic equation , quantum mechanics , evolutionary biology , biology , thermodynamics
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.