Homotopy analysis transform method for solving generalized Abel's fuzzy integral equations of the first kind

2015 ◽  
Author(s):  
Mohammad Ali Fariborzi Araghi ◽  
Samad Noeiaghdam
Keyword(s):  
Integral Equations ◽  
Fuzzy Integral ◽  
Transform Method ◽  
Homotopy Analysis

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

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
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.

scholarly journals Homotopy Analysis Method to Solve Two-Dimensional Nonlinear Volterra-Fredholm Fuzzy Integral Equations

2020 ◽  
Vol 4 (1) ◽  
pp. 9
Author(s):  
Atanaska Georgieva ◽  
Snezhana Hristova
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Homotopy Analysis Method ◽  
Approximate Solutions ◽  
Fredholm Integral Equations ◽  
Fuzzy Integral ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Fuzzy Solution

The main goal of the paper is to present an approximate method for solving of a two-dimensional nonlinear Volterra-Fredholm fuzzy integral equation (2D-NVFFIE). It is applied the homotopy analysis method (HAM). The studied equation is converted to a nonlinear system of Volterra-Fredholm integral equations in a crisp case. Approximate solutions of this system are obtained by the help with HAM and hence an approximation for the fuzzy solution of the nonlinear Volterra-Fredholm fuzzy integral equation is presented. The convergence of the proposed method is proved and the error estimate between the exact and the approximate solution is obtained. The validity and applicability of the proposed method is illustrated on a numerical example.

scholarly journals Homotopy analysis transform method for solving Abel’s integral equations of the first kind

2016 ◽  
Vol 7 (1) ◽  
pp. 483-495 ◽  
Author(s):  
Samad Noeiaghdam ◽  
Eisa Zarei ◽  
Hasan Barzegar Kelishami
Keyword(s):  
Integral Equations ◽  
Transform Method ◽  
Homotopy Analysis
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