Abstract
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.