Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method

The integral equations arise in many industrial fields, such as: electromagnetic fields and thermal problems. It is well-known that the problem of heat conduction with a variable heat transfer coefficient is reduced to the solution of a Volterra integral equation of second kind. In this paper, we focus on fuzzy linear Volterra integral equations of the second kind and propose a new method to solve them, namely “homotopy analysis method” (HAM). It is found that the HAM provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter h. The results illustrate the utility and the great potential of the HAM to solve fuzzy integral equations