Abstract
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 \(Li_{p}(z)\) 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 \(K=1\). We show that the proposed method achieves numerical convergence. The numerical experiment shows that this method is highly efficient and accurate.
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Acknowledgements
This research is supported by the Universiti Tun Hussein Onn Malaysia under the scheme GPPS H058. The second writer would also like to thank the Ministry of Education Malaysia and UTHM for providing financial support under the Fundamental Research Grant Scheme (FRGS) Vot K072.
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Kaharuddin, L.N., Phang, C. & Jamaian, S.S. Solution to the fractional logistic equation by modified Eulerian numbers. Eur. Phys. J. Plus 135, 229 (2020). https://doi.org/10.1140/epjp/s13360-020-00135-y
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DOI: https://doi.org/10.1140/epjp/s13360-020-00135-y