Nieto Roig, Juan José2022-09-022022-09-022022Fractional Calculus and Applied Analysis 25, 876–886 (2022). https://doi.org/10.1007/s13540-022-00044-01311-0454http://hdl.handle.net/10347/29199We solve a logistic differential equation for generalized proportional Caputo fractional derivative. The solution is found as a fractional power series. The coefficients of that power series are related to the Euler polynomials and Euler numbers as well as to the sequence of Euler’s fractional numbers recently introduced. Some numerical approximations are presented to show the good approximations obtained by truncating the fractional power series. This generalizes previous cases including the Caputo fractional logistic differential equation and Euler’s numberseng© The Author(s) 2022. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/Logistic differential equationFractional calculusGeneralized proportional fractional integralEuler numbersEuler fractional numbersjournal article10.1007/s13540-022-00044-01314-2224open access