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# Solution and Analysis of the Fuzzy Volterra Integral Equations via Homotopy Analysis Method

Ali. F. Jameel1,*, N. R. Anakira2, A. K. Alomari3, Noraziah H. Man1
1 School of Quantitative Sciences, Universiti Utara Malaysia, Kedah, Sintok, 06010, Malaysia
2 Department of Mathematics, Faculty of Science and Technology, Irbid National University, Irbid, 2600, Jordan
3 Department of Mathematics, Faculty of Science, Yarmouk University, Irbid, 21163, Jordan
* Corresponding Author: Ali. F. Jameel. Email:

Computer Modeling in Engineering & Sciences 2021, 127(3), 875-899. https://doi.org/10.32604/cmes.2021.014460

Received 29 September 2020; Accepted 25 February 2021; Issue published 24 May 2021

### 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.

### Keywords

Homotopy analysis method; convergence control parameter; fuzzy Volterra integral equations

Jameel, A. F., Anakira, N. R., Alomari, A. K., Man, N. H. (2021). Solution and Analysis of the Fuzzy Volterra Integral Equations via Homotopy Analysis Method. CMES-Computer Modeling in Engineering & Sciences, 127(3), 875–899.

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