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

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 equ...

Full description

Saved in:
Bibliographic Details
Published in:Fractal and fractional 2020-03, Vol.4 (1), p.9
Main Authors: Georgieva, Atanaska, Hristova, Snezhana
Format: Article
Language:English
Subjects:
convergence
error estimation
homotopy analysis method
Homotopy theory
Integral equations
Mathematical research
two-dimensional nonlinear volterra-fredholm fuzzy integral equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract4010009