Homotopy Perturbation Method Combined with ZZ Transform to Solve Some Nonlinear Fractional Differential Equations

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Lakhdar Riabi, Kacem Belghaba, Mountassir Hamdi Cherif, Djelloul Ziane, Homotopy Perturbation Method Combined with ZZ Transform to Solve Some Nonlinear Fractional Differential Equations, Int. J. Anal. Appl., 17 (3) (2019), 406-419.

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Lakhdar Riabi, Kacem Belghaba, Mountassir Hamdi Cherif, Djelloul Ziane

Abstract

The idea proposed in this work is to extend the ZZ transform method to resolve the nonlinear fractional partial differential equations by combining them with the so-called homotopy perturbation method (HPM). We apply this technique to solve some nonlinear fractional equations as: nonlinear time-fractional Fokker-Planck equation, the cubic nonlinear time-fractional Schrodinger equation and the nonlinear timefractional KdV equation. The fractional derivative is described in the Caputo sense. The results show that this is the appropriate method to solve somme models of nonlinear partial differential equations with time-fractional derivative.

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