Solutions of fractional logistic equations by Euler's numbers

In this paper, we solve in the convergence set, the fractional logistic equation making use of Euler's numbers. To our knowledge, the answer is still an open question. The key point is that the coefficients can be connected with Euler's numbers, and then they can be explicitly given. The constrained of our approach is that the formula is not valid outside the convergence set. The idea of the proof consists to explore some analogies with logistic function and Euler's numbers, and then to generalize them in the fractional case. (C) 2018 Elsevier B.V. All rights reserved.