Random solution behavior of two-dimensional volterra integral equations

This thesis consists of seven chapters. In the first chapter, basic information and literature related to the subject of the thesis are given. In the second chapter, basic concepts and definitions for probability theory and probability distributions are given. In the third chapter, the properties and classification of integral equations and their basic definitions are given. In the fourth chapter, basic definitions and properties of Differential Transformation Method (DTM), solution methods of Volterra integral equations and related examples are given. In the fifth chapter, the probability characters of the solution behaviors of random two–dimensional Volterra integral equations, mixed Volterra - Fredholm integral equations and two-dimensional random nonlinear Volterra integral equation systems obtained by selecting initial conditions or coefficients from continuous probability distributions were studied using the Differential Transformation Method (DTM). The graphs of the solutions obtained by calculating the expected value, variance and confidence intervals, which are the most useful of the probability characteristics of the obtained solutions, were plotted with the help of the Maple or Matlab program. In the sixth chapter, the relevant findings and discussions are examined. In the seventh chapter, the results discussed in the thesis are summarized.