Analytical and Numerical Methods for Solving Linear Fuzzy Volterra Integral Equation of the Second Kind

Integral equations, in general, play a very important role in Engineering and technology due to their wide range of applications. Fuzzy Volterra integral equations in particular have many applications such as fuzzy control, fuzzy finance and economic systems. After introducing some definitions in fuzzy mathematics, we focus our attention on the analytical and numerical methods for solving the fuzzy Volterra integral equation of the second kind. For the analytical solution of the fuzzy Volterra integral equation we have presented the following methods: The Fuzzy Laplace Transformation Method(FLTM), Fuzzy Homotopy Analysis Method(FHAM), Fuzzy Adomian Decomposition Method (FADM), Fuzzy Differential Transformation Method (FDTM), and the Fuzzy Successive Approximation Method (FSAM). For the numerical handling of the fuzzy Volterra Integral equation we have implemented various techniques, namely: Taylor expansion method, Trapezoidal method, and the variation iteration method. To investigate the efficiency of these numerical techniques we have solved some numerical examples. Numerical results have shown to be in a close agreement with the analytical ones. Moreover, the variation iteration method is one of the most powerful numerical techniques for solving Fuzzy Volterra integral equation of the second kind in comparison with other numerical techniques.