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Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation
Author(s) -
Akinyemi Lanre,
Iyiola Olaniyi S.,
Akpan Udoh
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6173
Subject(s) - mathematics , convergent series , nonlinear system , iterative method , homotopy analysis method , order (exchange) , series (stratigraphy) , homotopy perturbation method , differential equation , mathematical analysis , homotopy , mathematical optimization , pure mathematics , finance , economics , paleontology , physics , quantum mechanics , biology , power series
This paper presents analytical‐approximate solutions of the time‐fractional Cahn‐Hilliard (TFCH) equations of fourth and sixth order using the new iterative method (NIM) and q‐homotopy analysis method (q‐HAM). We obtained convergent series solutions using these two iterative methods. The simplicity and accuracy of these methods in solving strongly nonlinear fractional differential equations is displayed through the examples provided. In the case where exact solution exists, error estimates are also investigated.