https://doi.org/10.1140/epjp/s13360-020-00135-y
Regular Article
Solution to the fractional logistic equation by modified Eulerian numbers
Department of Mathematics and Statistics, Faculty of Applied Science and Technology, Universiti Tun Hussein Onn Malaysia, Pagoh, Johor, Malaysia
* e-mail: pchang@uthm.edu.my
Received:
24
August
2019
Accepted:
21
November
2019
Published online:
7
February
2020
In this paper, we propose a solution to the fractional logistic equation using Q-modified Eulerian numbers. These modified Eulerian numbers are obtained by modifying the Eulerian polynomials in two variables. Interestingly, these modified polynomials correspond to the polylogarithm 
of negative order and with a negative real argument, z. Our proposed method via the modified Eulerian numbers can provide the generalized solution when K is an arbitrary value, whereas in D’Ovidio and Paola (Phys A Stat Mech Appl 506:1081–1092, 2018), the solution obtained by using Euler’s numbers was only applicable when 
. We show that the proposed method achieves numerical convergence. The numerical experiment shows that this method is highly efficient and accurate.
© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature, 2020
