Local Fractional Operator for Analytical Solutions of the K(2, 2)-Focusing Branch Equations of Time-Fractional Order
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Local Fractional Operator (LFO) with respect to Caputo Derivative (CD) is employed for approximate-analytical solutions of the K(2, 2)-focusing branch equation of time-fractional order. The LFO technique is a projected version of the standard Differential Transform Method. The results obtained show that the method is simple, easy in implementation, and very much in line with the exact solutions at α = 1. Thus, the efficiency and robustness of the method. In addition, the proposed technique does not require the process or concept of Lagrange multipliers identification as in the case of the Variational Iteration Method.
KeywordsLocal fractional operator Modified DTM K(2, 2) equation
Mathematics Subject Classification26A33 34A25 68W25
Thanks to Covenant University for the provision of research resources. Also, sincere thanks to the anonymous referee(s) for their helpful remarks.
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Conflict of interest
Concerning the publication of this manuscript, no conflict of interest is declared by the authors.
- 7.Edeki, S.O., Akinlabi, G.O., Adeosun, S.A.: Approximate-analytical solutions of the generalized Newell–Whitehead–Segel model by He’s polynomials method. In: Proceedings of the World Congress on Engineering 2017, London, UK, vol. I, pp. 57–59 (2017)Google Scholar
- 10.Ziane, D., Belghaba, K., Cherif, M.H.: Fractional Homotopy perturbation transform method for solving the time-fractional KdV, K(2,2) and Burgers equations. Int. J. Open Problems Compt. Math. 8(2), 64–75 (2015)Google Scholar
- 15.Nyamoradi, N., Baleanu, D., Agarwal, R.P.: On a multipoint boundary value problem for a fractional order differential inclusion on an infinite interval. Adv. Math. Phys. 2013, Article ID 823961Google Scholar
- 16.Edeki, S.O., Akinlabi, G.O., Adeosun, S.A.: Analytic and numerical solutions of Time-fractional linear Schrödinger equation. Commun. Math. Appl. 7(1), 1–10 (2016)Google Scholar
- 18.Zhou, J.K.: Differential transformation and its application for electrical circuits. Huarjung University Press, Wuuhahn (1986)Google Scholar