On Global Existence of Solution of Nonlinear Integral Equations with Applications to Volterra & Fredholm Integral Equations

Abstract

The aim of this dissertation was to study global existence of solutions of nonlinear integral equations with applications to Volterra and Fredholm integral equations using some analytical and numerical methods. Chapter one includes introduction of the integral equation(IE) and construction methods of the IE . Chapter two includes existence of solutions of linear integral equations using Adomain decomposition method and Adomain modified decomposition method and noice terms phenomenon and fuzzy integral equation and homotopy perturbation method. Chapter three includes existence of solutions of nonlinear integral equation using successive approximation method and Adomain decomposition method and Laplace transform method and direct computational method. Chapter four includes existence and uniqueness of continuous solutions of linear and nonlinear Volterra-Fredholm integral equation in cone metric space. Chapter five includes numerical methods (variation iteration method and homotopy perturbation method ) for linear and nonlinear Fredholm integral equation.