TY - JOUR
T1 - Analytical Treatment of Abel Integral Equations by Optimal Homotopy Analysis Transform Method
AU - Mohamed S. Mohamed
JO - Journal of Information and Computing Science
VL - 1
SP - 019
EP - 028
PY - 2024
DA - 2024/01
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jics/22561.html
KW -  integeral  equation,  Abel  integral  equation,  optimal  homotopy  analysis  transform  method,  
Laplace transform. 

AB -  In  this  paper,  a  user  friendly  algorithm  based  on  the  optimal  homotopy  analysis  transform 
method  (OHATM)  is  proposed  to  solve  a  system  of  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  to  the  exact  solutions.  Illustrative  numerical  examples  are  given  to 
demonstrate the efficiency and simplicity of the proposed method in solving such types of systems of Abel's 
integral  equations.  Finally,  several  numerical  examples  are  given  to  illustrate  the  accuracy  and  stability  of 
this  method.  Comparison  of  the  approximate  solution  with  the  exact  solutions  we  show  that  the  proposed 
method is very efficient and computationally attractive.