Existence of solution for an infinite system of nonlinear integral equations via measure of noncompactness and homotopy perturbation method to solve it

2018 ◽  
Vol 343 ◽  
pp. 341-352 ◽  
Author(s):  
Bipan Hazarika ◽  
H.M. Srivastava ◽  
Reza Arab ◽  
Mohsen Rabbani
Keyword(s):  
Perturbation Method ◽  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Existence Of Solution ◽  
Nonlinear Integral Equations ◽  
Homotopy Perturbation

scholarly journals Solvability of an infinite system of integral equations on the real half-axis

2020 ◽  
Vol 10 (1) ◽  
pp. 202-216
Author(s):  
Józef Banaś ◽  
Weronika Woś
Keyword(s):  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Main Tool ◽  
Supremum Norm ◽  
Nonlinear Integral Equations ◽  
Measures Of Noncompactness ◽  
System Of Integral Equations ◽  
The Real ◽  
Half Axis

Abstract The aim of the paper is to investigate the solvability of an infinite system of nonlinear integral equations on the real half-axis. The considerations will be located in the space of function sequences which are bounded at every point of the half-axis. The main tool used in the investigations is the technique associated with measures of noncompactness in the space of functions defined, continuous and bounded on the real half-axis with values in the space l∞ consisting of real bounded sequences endowed with the standard supremum norm. The essential role in our considerations is played by the fact that we will use a measure of noncompactness constructed on the basis of a measure of noncompactness in the mentioned sequence space l∞. An example illustrating our result will be included.

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.

Sign in / Sign up

Export Citation Format

Share Document