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.
