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
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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