Abstract
In this paper, we generalize the formula of Sumudu transform to the conformable fractional order and some interesting and important rules of this transform and conformable fractional Laplace transform are derived and discussed. Moreover, we present the general analytical solution of a singular and nonlinear conformable fractional Poisson- Boltzmann differential equation based on the conformable fractional Sumudu transform. Also, our proposed method is applied successfully for obtaining the general solutions of some linear and nonhomogeneous conformable fractional differential equations. Finally, the results show that our proposed method is an efficient and can be applied for finding the general solutions of the all cases realted to the conformable fractional differential equations.