Application of new iterative transform method and modified fractional homotopy analysis transform method for fractional Fornberg-Whitham equation

In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo–Fabrizio and Atangana–Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called [Formula: see text]-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.

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A novel solution procedure for fuzzy fractional heat equations by homotopy analysis transform method

Neural Computing and Applications ◽

10.1007/s00521-012-0855-z ◽

2012 ◽

Vol 23 (2) ◽

pp. 269-271 ◽

Cited By ~ 19

Author(s):

Ahmed Salah ◽

Majid Khan ◽

Muhammad Asif Gondal

Keyword(s):

Solution Procedure ◽

Heat Equations ◽

Transform Method ◽

Homotopy Analysis

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On exact solutions for time-fractional Korteweg-de Vries and Korteweg-de Vries-Burger’s equations using homotopy analysis transform method

Chinese Journal of Physics ◽

10.1016/j.cjph.2019.11.004 ◽

2020 ◽

Vol 63 ◽

pp. 149-162 ◽

Cited By ~ 26

Author(s):

K.M. Saad ◽

Eman. H.F. AL-Shareef ◽

A.K. Alomari ◽

Dumitru Baleanu ◽

J.F. Gómez-Aguilar

Keyword(s):

Exact Solutions ◽

Transform Method ◽

De Vries ◽

Homotopy Analysis ◽

Burger's Equations

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Approximate Solutions of the Generalized Abel’s Integral Equations Using the Extension Khan’s Homotopy Analysis Transformation Method

Journal of Applied Mathematics ◽

10.1155/2015/357861 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 3

Author(s):

Mohamed S. Mohamed ◽

Khaled A. Gepreel ◽

Faisal A. Al-Malki ◽

Maha Al-Humyani

Keyword(s):

Exact Solutions ◽

Integral Equations ◽

Method Comparison ◽

Approximate Solutions ◽

Transformation Method ◽

Theory Of Elasticity ◽

Transform Method ◽

Numerical Examples ◽

Homotopy Analysis ◽

User Friendly

User friendly algorithm based on the optimal homotopy analysis transform method (OHATM) is proposed to find the approximate solutions to generalized Abel’s integral equations. The classical theory of elasticity of material is modeled by the system of Abel integral equations. It is observed that the approximate solutions converge rapidly to the exact solutions. Illustrative numerical examples are given to demonstrate the efficiency and simplicity of the proposed method. Finally, several numerical examples are given to illustrate the accuracy and stability of this method. Comparison of the approximate solution with the exact solutions shows that the proposed method is very efficient and computationally attractive. We can use this method for solving more complicated integral equations in mathematical physical.

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