In this paper, we proceed on to develop the classical Natural transform to fractional order in the sense of conformable derivative and set the basic concepts in this new interesting fractional transform version. The conformable fractional Natural transform of certain functions, properties and relationships are derived and discussed. Furthermore, we present the general analytical solution of a generalized conformable Bernoulli’s fractional differential equation based on the new version and Adomain polynomial method. This method is also applied successfully to find the general solutions of some linear and nonlinear conformable fractional differential equations. Finally, the results show that our new approach is simple, accurate and effective.

在本文中，我们将继续从顺应性导数的意义上将经典的自然变换发展为分数阶，并在此新的有趣的分数变换版本中设置基本概念。推导并讨论了某些函数，属性和关系的符合分数自然变换。此外，我们提出了基于新版本和Adomain多项式方法的广义一致的Bernoulli分数阶微分方程的一般解析解。该方法也成功地用于寻找一些线性和非线性一致分数阶微分方程的一般解。最后，结果表明我们的新方法简单，准确，有效。