@Article{cmes.2021.014460,
AUTHOR = {Ali. F. Jameel, N. R. Anakira, A. K. Alomari, Noraziah H. Man},
TITLE = {Solution and Analysis of the Fuzzy Volterra Integral Equations via Homotopy Analysis Method},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {127},
YEAR = {2021},
NUMBER = {3},
PAGES = {875--899},
URL = {http://www.techscience.com/CMES/v127n3/42606},
ISSN = {1526-1506},
ABSTRACT = {Homotopy Analysis Method (HAM) is semi-analytic method to solve the linear and nonlinear mathematical
models which can be used to obtain the approximate solution. The HAM includes an auxiliary parameter, which
is an efficient way to examine and analyze the accuracy of linear and nonlinear problems. The main aim of this
work is to explore the approximate solutions of fuzzy Volterra integral equations (both linear and nonlinear) with
a separable kernel via HAM. This method provides a reliable way to ensure the convergence of the approximation
series. A new general form of HAM is presented and analyzed in the fuzzy domain. A qualitative convergence
analysis based on the graphical method of a fuzzy HAM is discussed. The solutions sought by the proposed method
show that the HAM is easy to implement and computationally quite attractive. Some solutions of fuzzy second
kind Volterra integral equations are solved as numerical examples to show the potential of the method. The results
also show that HAM provides an easy way to control and modify the convergence area in order to obtain accurate
solutions.},
DOI = {10.32604/cmes.2021.014460}
}