scholarly journals A local fractional homotopy perturbation method for solving the local fractional Korteweg-de Vries equations with non-homogeneous term

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1495-1501 ◽  
Author(s):  
Yong-Ju Yang ◽  
Shun-Qin Wang
Keyword(s):  
Perturbation Method ◽  
Initial Value Problems ◽  
Homotopy Perturbation Method ◽  
Validity And Reliability ◽  
Initial Value ◽  
Homotopy Perturbation ◽  
De Vries

In this paper, a local fractional homotopy perturbation method is presented to solve the boundary and initial value problems of the local fractional Korteweg-de Vries equations with non-homogeneous term. In order to demonstrate the validity and reliability of the method, two types of the Korteweg-de Vries equations with non-homogeneous term are proposed.

Homotopy Perturbation Method for a Class of Nonlinear Singular System of Initial Value Problems

2020 ◽  
Vol 12 (1) ◽  
pp. 60-64
Author(s):  
Priti Pathak ◽  
Amit K. Barnwal
Keyword(s):  
Perturbation Method ◽  
Convergence Analysis ◽  
Initial Value Problems ◽  
Homotopy Perturbation Method ◽  
Singular System ◽  
Initial Value ◽  
Recursive Scheme ◽  
Homotopy Perturbation ◽  
Nonlinear Singular System

In this paper, a method based on homotopy perturbation method is used to establish the recursive scheme for the solution of nonlinear singular system of initial value problems. The convergence analysis of the proposed method is also shown. The accuracy and efficiency of the proposed method are demonstrated through various examples.

scholarly journals Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control

2019 ◽  
Vol 38 (2) ◽  
pp. 706-727 ◽  
Author(s):  
Reza Novin ◽  
Mohammad Ali Fariborzi Araghi
Keyword(s):  
Perturbation Method ◽  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
The Novel ◽  
Validity And Reliability ◽  
Hypersingular Integral ◽  
Homotopy Perturbation ◽  
Hypersingular Integral Equations ◽  
Ideal Tool ◽  
Novel Method

This paper attempts to propose and investigate a modification of the homotopy perturbation method to study hypersingular integral equations of the first kind. Along with considering this matter, of course, the novel method has been compared with the standard homotopy perturbation method. This method can be conveniently fast to get the exact solutions. The validity and reliability of the proposed scheme are discussed. Different examples are included to prove so. According to the results, we further state that new simple homotopy perturbation method is so efficient and promises the exact solution. The modification of the homotopy perturbation method has been discovered to be the significant ideal tool in dealing with the complicated function-theoretic analytical structures within an analytical method.

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