Fuzzy Fredholm Integral Equation of the Second Kind

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Type: 
Thesis
Year: 
2014
Students: 
Muna Shaher Yousef Amawi
Abstract: 

Fuzzy Fredholm integral equations of the second kind have received considerable attention due to the importance of these types of equations in studies associated with applications in mathematical physics and fuzzy financial and economic systems. After addressing the basic concepts of fuzzy integral equations, we have investigated the analytical and the numerical aspects of the fuzzy Fredholm integral equation of the second kind. The analytical methods include: Fuzzy Laplace transform method, Homotopy analysis method (HAM), Adomain decomposition method (ADM) and Fuzzy differential transformation method (FDTM). For the numerical treatment of the fuzzy integral equation of the second kind, we have employed the Taylor expansion method and the trapezoidal method. Some numerical test cases are included. A comparison between the analytical and the numerical methods has been presented. Numerical results have shown to be in a closed agreement with the analytical ones.